Rational And Irrational Numbers
Class 8th Mathematics (new) MHB Solution
Practice Set 1.1- Show the following numbers on a number line. Draw a separate number line for each…
- Show the following numbers on a number line. Draw a separate number line for each…
- Show the following numbers on a number line. Draw a separate number line for each…
- Show the following numbers on a number line. Draw a separate number line for each…
- Observe the number line and answer the questions.(1) Which number is indicated by point…
Practice Set 1.2- Compare the following numbers.-7, -2
- Compare the following numbers.0, -9/5
- Compare the following numbers.8/7, 0
- Compare the following numbers. {-5}/{4} , frac {1}/{4}
- Compare the following numbers. {40}/{29} , frac {141}/{29}
- Compare the following numbers. - {17}/{20} , frac {-13}/{20}
- Compare the following numbers. {15}/{12} , frac {7}/{16}
- Compare the following numbers. {-25}/{8} , frac {-9}/{4}
- Compare the following numbers. {12}/{15} , frac {3}/{5}
- Compare the following numbers. {-7}/{11} , frac {-3}/{4}
Practice Set 1.3- Write the following rational numbers in decimal form.9/37
- Write the following rational numbers in decimal form.18/42
- Write the following rational numbers in decimal form.9/14
- Write the following rational numbers in decimal form.-103/5
- Write the following rational numbers in decimal form.-11/13
Practice Set 1.4
- Show the following numbers on a number line. Draw a separate number line for each…
- Show the following numbers on a number line. Draw a separate number line for each…
- Show the following numbers on a number line. Draw a separate number line for each…
- Show the following numbers on a number line. Draw a separate number line for each…
- Observe the number line and answer the questions.(1) Which number is indicated by point…
- Compare the following numbers.-7, -2
- Compare the following numbers.0, -9/5
- Compare the following numbers.8/7, 0
- Compare the following numbers. {-5}/{4} , frac {1}/{4}
- Compare the following numbers. {40}/{29} , frac {141}/{29}
- Compare the following numbers. - {17}/{20} , frac {-13}/{20}
- Compare the following numbers. {15}/{12} , frac {7}/{16}
- Compare the following numbers. {-25}/{8} , frac {-9}/{4}
- Compare the following numbers. {12}/{15} , frac {3}/{5}
- Compare the following numbers. {-7}/{11} , frac {-3}/{4}
- Write the following rational numbers in decimal form.9/37
- Write the following rational numbers in decimal form.18/42
- Write the following rational numbers in decimal form.9/14
- Write the following rational numbers in decimal form.-103/5
- Write the following rational numbers in decimal form.-11/13
Practice Set 1.1
Question 1.Show the following numbers on a number line. Draw a separate number line for each example.
![](data:image/png;base64,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)
Answer:For
the number line will be:
![](data:image/jpeg;base64,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For
the number line will be:
![](data:image/jpeg;base64,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)
For
the number line will be:
![](data:image/jpeg;base64,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)
Question 2.Show the following numbers on a number line. Draw a separate number line for each example.
![](data:image/png;base64,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)
Answer:For
the number line will be:
![](data:image/jpeg;base64,/9j/4AAQSkZJRgABAQEAYABgAAD/2wBDAAoHBwgHBgoICAgLCgoLDhgQDg0NDh0VFhEYIx8lJCIfIiEmKzcvJik0KSEiMEExNDk7Pj4+JS5ESUM8SDc9Pjv/2wBDAQoLCw4NDhwQEBw7KCIoOzs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozv/wAARCABvAlkDASIAAhEBAxEB/8QAHAABAAMBAQEBAQAAAAAAAAAAAAUGBwEEAgMI/8QAPRAAAQMDAQcCBQAIAwkAAAAAAAECAwQFEQYSEyExVJPSQVEHFCJhcRUyN0JSdIHBFmKxIzNDc5KhstHh/8QAGgEBAAMBAQEAAAAAAAAAAAAAAAIDBAEFBv/EACoRAQACAgEDAwIGAwAAAAAAAAABAgMRBBIhMQVBURMiFFJxgZHwYXKh/9oADAMBAAIRAxEAPwDZgAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAeC+XNtmslbc3RrJ8rC6RI0XG2qJwT+q8Cmx/FZ75qeB2kL1HLUPbHGj4kajnr6Iql8qKeGqhdDURtljdjaa5MouFyVaxVyag1veqiT6orM5tHStXk1yoqyP/ACq4T8J9wLa1VVqK5MKqcUzyOgAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAADyUVrobdLUy0dMyF9XKs07mp/vHr6qfVdTMqqdWyVE1O1q7SvilWNUx7r7EU2gt0ixoy/VjllXEaNuCrt/jjxAngfLG7EbWbTnbKImXLlV/J9AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAITUmqaLTcDHT5lnkX6IWr9Sp6r9kOTMRG5W4cOTNeMeONzKbB5bdcaW60MdZRypJFInBfVF9l9lPUdQtW1bTW0amAABEBzKZxnj7HQAAAAHEVF5LkDoAAAHFVETKrhAOgAAAAAOZTOM8fY6AAAAHmr6+mtlFJWVkqRQxplVX/RPdSM03quh1JHIkGYp41XahevHZ9FT3Objel9ePltinLWs9MeZTgAOqAA4qonNcAdAAAAAeO8RvlstdFGmXvp5GtRVxlVaqIZ5ZrVp/QVxtE1dYPlZ7iqQx1i1O+3UqonBU/dzleKZL/fLVDfbNV2meR8cdVErHOYv1N+5XqjRVRdZbPDdamBKCzOa+CCna7MrmoiN21cvJMck5gXEAAADiKiplFygHQAAAOKqJzXAHQAAAOKuEyvBAOgrUOurRNqB1qbJhv6rahV+hz/4f/pZTkTE+F+bj5cExGSsxuNwAA6oADiKiplFygHQAAAOKqJzXAHQAAAAAHMpnGePsdAAAAAcRUVMouUA6AAABAah1hb9OzQwTbUs0jk2mM5sZ/Ev/o5MxHldhwZM9+jHG5T4PxpaqCtpo6mmlbLDIm017V4Kh+x1VMTE6lHbq9dVR9l3kN1euqo+y7yJE/OoY+Wnkjjfu3uaqNfjOyvuHEZBJdauBZKauoXtyrUduXYynD+L3MX1dS6ghvUyXZ6vqHOyrmcNpvorV9vsbjbralt3jI5nvhfsqjXrlUVEwvH74Q/G+afoNQUzYa2NcsdlkjeDm++F+5C1Znw9L0/l0497Vyb6bRqZjtMfozr4Z0mpd++amnijosYm3rFVr3fZM8/uaRur11VH2XeR66WlgoqaOmpomxQxpstY1OCIfsdrGo0q53Kjk5pyRGo/7+/+Udur11VH2XeQ3V66mj7LvIkQSYmJVVo1u7XrpEbUOqfm9plQ1HbpI9rguc42dn0/oa5ur11VH2XeRIg0Zs85encRGo12QrXp2jt1euqo+y7yG6vXVUfZd5EiDOmq+qqXU8+mq2O31EC1Do/pbDG5r3JlNpGrnnjJUfhjbdVUtZWPej6ajdGiKlVG7Dn5/dRV54zlTVgaKZ5riti1Hf390Jru0WR26vXVUfZd5DdXrqqPsu8iRBnTR26vXVUfZd5Ge/E63aqqZaJ0e1U0bWqitpY3fTJnm5EXPLkv5NTBdgyzhyRkiN6+Ub16q6VTSFJqen0vRRV9RCydrV+mdjnPa3K7KOXPPGCa3V66qj7LvIkQV2t1WmXYjUI7dXrqqPsu8gkV6zxqaPH/ACXeRIgi6xJbRrf/AB7vNmoWq+b2vmMO3W72uec42dn0/oa5ur11NH2XeRIg0Z885uncRGo12QrXp2jt1euqo+y7yG6vXVUfZd5EiDOmyr4k0upEmhmqpopLenBm6YqNY7/Mmef3KvpymvlReoG2iRraprso9Grhqequ+xvFTTQ1lNJT1EbZYpG7LmOTKKh4LHp236fp3xUUa5kdl8j+Ll9kz7IVTjmbbfScb1mmLhThmv3R2j4n9f73dZFfEY3bqqJXY4qkLuf/AFH1ur11VH2XeRIgtfNo7dXrqqPsu8jO/idbdVVNVRvjR9TRoxU2aWN2GyZ5uRFzyxhTVQXYM04ckZIjevlG9equlW0pS6ng0zQxV9RA2obHxbMxzntTPBHLnnjBMbq9dVR9l3kSIKrTuZl2OyO3V66qj7LvIJFeupo+y7yJEHHWIU9t1knxBaiySfPpU7x8i52N1tfrc8bGOGP6Gvbq9dTR9l3kUeC+bXxZe7a/2T3LSc/ZMf8AkhpJbk5E59biI127NnL4U8SaR+asW/efKO3V66qj7LvIbq9dVR9l3kSIKmNUtY0mqKjS9XFb6iF0yomWwRua9zc/UjVzzwVv4YW7VVKta6XapqRyN2W1cbvqflcq1FXKcOa/g1EGiuea4bYtR3ne/dCa7tFkdur11VH2XeQ3V66qj7LvIkQZ00dur11VH2XeRnPxNtuq6mvpHsR9TRpHhraSN2GyZXOUReapjCmrguwZpw5IyRETr5RvXqrpWdMUupoNN0MdfUQJUNiw5Jo3OeieiOXPFcYJXdXrqqPsu8iRBVM7naSO3V66qj7LvIgdY0uqZrDK2hqadyf8VkUbke5nqicS3gjMbjS3Dl+lkrk1vT+cGx1bnoxqsV6rhERi5VTadNUuqYbHAy4VVLvkTgkkble1vojlzxU9kOlrPDf33aOBvzKpnY/da71cie5NFdKTXy9n1X1SnMpWmOvaO87+fiP73R26vXVUfZd5DdXrqqPsu8iRBa8FUNa0mqKjS9VHQTxPlXZ2mQRua9zM/UiLn2K/8MLdqmlZWumVaakfs7tlXG7i/jlWoq5ThzNPBornmuGcWo7zvfuhNd26kdur11VH2XeQ3V66qj7LvIkQZ00dur11VH2XeRm3xLtmq6m6Ur2pJVUiRYYlJG7DX5XOURea8OJrQL+PmnDkjJEROvlG9equlb03Tamh07Qx19TTpUtiRHpLG5z09kcueK4xkk91euqo+y7yJEFMzudpI7dXrqqPsu8jm6vXVUfZd5EkDgxKz2jW7NdRySNqG1LajanqHo7dKzPFVXOFaqck/Brm6vXU0fZd5EiDRnzzmmJmIjUa7IUp0o7dXrqqPsu8hur11VH2XeRIgzpqbrij1RU6XqI6CaKR6ubvGU8bmvcz95E4kL8Mbfqmlp61Z1+XpHq3dMq43Kqu45VqZyicvyaYDRXPMYZxajvO9+6E1+7qR26vXVUfZd5DdXrqqPsu8iRBnTRVRDf1p5Egq6FsqtXYV0LsIvp6mIXenvEF1qGXRyfN7eZFeiqqr75zyP6EIi96Ztt/fA+tiy+FyKjmrhXJ6tX7Fd6zaOz2fSfUKcPJP1I7T7x5Uv4b0mpW080sc8Mdvf8AqNmjVdp3u3jw+5et1euqo+y7yPdFFHDE2KJjWMYmGtamERD7JVjUaYeZyfxOe2XWtgAJMgAZJc/nr63V+oP0rW009indHQRwzK2Nm7TK5byXP3A1sEfYK9910/b7hImH1NNHK5E91aiqSAAAAAAAAAAAAAAAAAAAAAAAAAAAADP/AIoah1FbLXUxWWlfTwQwtlqLkrsbGXYRjP8AN7+yKaAVj4jW6su2hblQ0FO+oqZWsRkbObsPaq/9kAn6B7pLfTPe5XOdE1VVfVcIeg89Cx0dvpo3t2XNiajkX0VEQ9AAAAAAAPl21srs42scM+59ADIIdLXJutfkEq4fm40SqWTjsquUX8+pryZwmeZTYv2szfyKf2LmV44iNva9X5OTNOLr/LE/z5AAWPFAAAAAAAAAAAPiVr3wvbG/Ye5qo12M7K+59n5VG+Sml+XRqzbC7tHrw2scM/bIGTXew0+m71Y6O13KrrtVVFa2Son3rsvhyqu225VEbj/RTXjMdN6Y13YrjUV0lPY6urrZtqprJpZHS7OeLW8MIiexpwAAAAAAAAAAAAAAAAAAAAAAAAAAACpa5iuDKb9If4hntFrpIldN8pFtTSPzhvH2+xbSs6juGprXdIJ7daW3a1viVs1PGqNlbJ6LleCtA/TQVwuV00bQVt2eySqlaqq9qp9TcrsquOCLjGSxFX+H1irrBpx0NwayKoqamSpdAxctg21yjEX7FoAAAAZvdtI6mhqL/brMyjktuoZN5JPLIrX0quTD/p/ez6GkADy2yhjtlrpaCJcx00LYmqvqjUx/Y9QAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAFMi/azN/Ip/YuZTIv2szfyKf2LmQp7vS9Q84v9KgAJvNAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAUyL9rM38in9i5nhSz0Tby67pGvzbot0r9pcbP4PcRrGmvlZ65ujp9qxH8AAJMgAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAD//2Q==)
For
the number line will be:
![](data:image/jpeg;base64,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)
For
the number line will be:
![](data:image/jpeg;base64,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)
Question 3.Show the following numbers on a number line. Draw a separate number line for each example.
![](data:image/png;base64,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)
Answer:For
the number line will be:
![](data:image/jpeg;base64,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)
For
the number line will be:![](data:image/jpeg;base64,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)
Question 4.Show the following numbers on a number line. Draw a separate number line for each example.
![](data:image/png;base64,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)
Answer:For
the number line will be:
![](data:image/jpeg;base64,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For
the number line will be:![](data:image/png;base64,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)
Question 5.Observe the number line and answer the questions.
![](data:image/png;base64,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)
(1) Which number is indicated by point B?
(2) Which point indicates the number
?
(3) State whether the statement, ‘the point D denotes the number 5/2, is true or false.
Answer:As each part between integers divided into 4 parts on the number line hence each part equals
.
(1) Which number is indicated by point B?
Now point B is 10 places to left i.e. in the negative side of number line hence point B is
.
(2) Which point indicates the number
?
Now
can also be written as
,Which means seven places to right i.e. Point C.
(3) State whether the statement, ‘the point D denotes the number 5/2, is true or false.
Now point D is 10 places away from zero i.e. it is
which can also be written as
.
Hence the above statement is true.
Show the following numbers on a number line. Draw a separate number line for each example.
Answer:
For the number line will be:
For the number line will be:
For the number line will be:
Question 2.
Show the following numbers on a number line. Draw a separate number line for each example.
Answer:
For the number line will be:
For the number line will be:
For the number line will be:
Question 3.
Show the following numbers on a number line. Draw a separate number line for each example.
Answer:
For the number line will be:
For the number line will be:
Question 4.
Show the following numbers on a number line. Draw a separate number line for each example.
Answer:
For the number line will be:
For the number line will be:
Question 5.
Observe the number line and answer the questions.
(1) Which number is indicated by point B?
(2) Which point indicates the number ?
(3) State whether the statement, ‘the point D denotes the number 5/2, is true or false.
Answer:
As each part between integers divided into 4 parts on the number line hence each part equals .
(1) Which number is indicated by point B?
Now point B is 10 places to left i.e. in the negative side of number line hence point B is.
(2) Which point indicates the number ?
Now can also be written as
,Which means seven places to right i.e. Point C.
(3) State whether the statement, ‘the point D denotes the number 5/2, is true or false.
Now point D is 10 places away from zero i.e. it is which can also be written as
.
Hence the above statement is true.
Practice Set 1.2
Question 1.Compare the following numbers.
-7, -2
Answer:Now if there are two numbers, a and b such that a>b then
-a<-b.
Therefore, as 7>2
Hence -7<-2.
Question 2.Compare the following numbers.
0, -9/5
Answer:As -9/5 is a negative quantity, it will be always less than zero.
0>-9/5.
Question 3.Compare the following numbers.
8/7, 0
Answer:As 8/7 is a positive quantity, it will always be greater than zero.
0<8/7.
Question 4.Compare the following numbers.
![](data:image/png;base64,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)
Answer:As the denominator is same, we just need to check which number in the numerator is greater.
As -5 < 1
![](data:image/png;base64,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)
Question 5.Compare the following numbers.
![](data:image/png;base64,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)
Answer:As the denominator is same, we just need to check which number in the numerator is greater.
As 40 < 141
![](data:image/png;base64,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)
Question 6.Compare the following numbers.
![](data:image/png;base64,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)
Answer:Now if there are two numbers, a and b such that a>b then
-a<-b.
Therefore, as 17>13
Hence -17<-13.
Also, As the denominator is same, we just need to check which number in the numerator is greater.
As -17 < -13
![](data:image/png;base64,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)
Question 7.Compare the following numbers.
![](data:image/png;base64,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)
Answer:![](data:image/png;base64,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)
As we have made denominator equal we now just need to check whose numerator is greater.
Therefore, as 60>21.
![](data:image/png;base64,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)
Hence,![](data:image/png;base64,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)
Question 8.Compare the following numbers.
![](data:image/png;base64,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)
Answer:![](data:image/png;base64,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)
As we have made denominator equal we now just need to check whose numerator is greater.
Therefore, as -25<-18.
Hence
.
Question 9.Compare the following numbers.
![](data:image/png;base64,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)
Answer:![](data:image/png;base64,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)
As we have made denominator equal we now just need to check whose numerator is greater.
Therefore, as 12 >9.
![](data:image/png;base64,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)
Hence,![](data:image/png;base64,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)
Question 10.Compare the following numbers.
![](data:image/png;base64,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)
Answer:![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAWwAAAAoCAMAAADt/zBFAAAAAXNSR0IArs4c6QAAAIFQTFRFAAAAAAAAAAA6AABmADo6ADpmADqQAGa2OgAAOgA6OjoAOjqQOmaQOma2OpC2OpDbZgAAZgA6ZjoAZjo6ZjpmZmZmZmaQZpDbZrbbZrb/kDoAkGY6kLbbkNv/tmYAttv/tv//25A627Zm27aQ29u22////7Zm/9uQ/9u2//+2///bok+hWgAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAD6klEQVRoQ+1a23bbIBBEbtO4rVO77i1xEqWOa1nS/39gASEWJGC1CPn0Ag8xJ9Yso9GygDyM5ZYV+A8UOBayvTvT7nUC7Lh6psVkrD3ti+JGwl4/FMXqhydAK77trqM0HHb60geF3vQRIL5npPKBB7usxV9Kw2GXNV3ssrhn9e7NT8aOq3sueLF1cypXT6w+kONjsHpfiLF5gx5JFE0rNNJRjUGJzK/VsOar4qg++XfN7htZDFbeiqjFA2sPosdKz4TT19EI27AR6cvmRd0R9EgDQPwAwWbnyaDwUABrDzdC7WZ3pxHltqKLLdGVIbaU3NPKuAzRMAdpSB+jR9KbJ4im5SYYUV0FAwPWHngONjvQpvp4jhVbcqx4QWGvgcdVP25eiDLI+mDARqSNuRorNsT3EFRzlkrdgnHiv/a3epVtPj+zSLHV+nFa8wXSuwQ2u6LYENd0OfUs2IC0WRjjxIb4uld2GxDeursR83ZCC8Pag7GjaQ+8LnGxj2jgYVBerWVJu6z5h6jefRtdeFpPKSNhmEVaTlYdc9oyNgrPgJaboG8ZQh6ADbN4V/3TRMUejqGmi5zhXPjQjrTy7VXCvE3YbLEdQ0F8F0GZRPRmw+SMtKWJKiNlV4pU+Q+ugfN5j0lTM9shG9ByEZy7qosB+7XGLKMxYh/F86q2fU575lxXaiZWP9BjCHOQniU2xPcSnL3v67XW+ahuL2KPc3nPF5G2lOX609l7qGnFeaYO1hjXTB3AVJEy91DGBiuCPcT3EoxJQJFX5lah/t6l9EV9dstuYDfhqVpqvRF5Kw/kT57r6ke+V7kj70Zs2Ih0K6IWb/k7AuiRyivEjyRIGi1fnBXICmQFsgJZgaxAViAr8JcpMH67kuIGlomqmS0cnkXG1+/87A4mqAeG/BuJigbt8VclDYOloo+Jm7+/igKRMwbhtkzUP72MXOWB5UGyAlmBf16BSOvPdBj5fTAAECg5cvcww7DpN+ZJDT/9SOsPAUb2QwEAgZIjd+oEYYQb82jtpx9p/fHBUvihwECFWKminFa2QSu9Fcrwf7n4Rf7Y5oSl8EOBgQqxUkU6rUzYAlaoMP2UYuufe/UUI/uhAIBAyZE7TjYsuRUKoZ9UbKH2LD8UGKgQK1Wk02oIS2yFwuinFZurHeWHUlMBDFSIlWq608pax8awpO4clP6SYpP9UABAoOTIqoiMDFpJxUbppxU7hR8KvBGIuSKB92IBK1SIflKxk/ihrih2aiuUXIK1j2acDJPPa/Ym3glzWYuQA5vjaDCZ0ewTZHIrlH1AHfCLtP74YEn8UGCgQqxUMU4rkXlg0EpvhTLDW/x+AwbPii3Ft+mJAAAAAElFTkSuQmCC)
As we have made denominator equal we now just need to check whose numerator is greater.
Therefore, as -28>-33.
Hence
.
Compare the following numbers.
-7, -2
Answer:
Now if there are two numbers, a and b such that a>b then
-a<-b.
Therefore, as 7>2
Hence -7<-2.
Question 2.
Compare the following numbers.
0, -9/5
Answer:
As -9/5 is a negative quantity, it will be always less than zero.
0>-9/5.
Question 3.
Compare the following numbers.
8/7, 0
Answer:
As 8/7 is a positive quantity, it will always be greater than zero.
0<8/7.
Question 4.
Compare the following numbers.
Answer:
As the denominator is same, we just need to check which number in the numerator is greater.
As -5 < 1
Question 5.
Compare the following numbers.
Answer:
As the denominator is same, we just need to check which number in the numerator is greater.
As 40 < 141
Question 6.
Compare the following numbers.
Answer:
Now if there are two numbers, a and b such that a>b then
-a<-b.
Therefore, as 17>13
Hence -17<-13.
Also, As the denominator is same, we just need to check which number in the numerator is greater.
As -17 < -13
Question 7.
Compare the following numbers.
Answer:
As we have made denominator equal we now just need to check whose numerator is greater.
Therefore, as 60>21.
Hence,
Question 8.
Compare the following numbers.
Answer:
As we have made denominator equal we now just need to check whose numerator is greater.
Therefore, as -25<-18.
Hence.
Question 9.
Compare the following numbers.
Answer:
As we have made denominator equal we now just need to check whose numerator is greater.
Therefore, as 12 >9.
Hence,
Question 10.
Compare the following numbers.
Answer:
As we have made denominator equal we now just need to check whose numerator is greater.
Therefore, as -28>-33.
Hence.
Practice Set 1.3
Question 1.Write the following rational numbers in decimal form.
9/37
Answer:![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAM4AAAF9CAIAAADDVMD8AAAAAXNSR0IArs4c6QAAAAlwSFlzAAAOxAAADsMB2mqY3AAAFKlJREFUeF7tnTt22zoQhum7FsmFj1bgrEB2k8ptOqWUm3Qu091GLq0ubSo3V16BvQKfFJH34gsSepAgSIAEOHjMzy4xgAH++QwSMDBz8fn5WeCBAtMr8M/0JmABCpQKADVwQKQAUCMSGmaAGhggUgCoEQkNM0ANDBApANSIhIYZoAYGiBQAakRCwwxQAwNECgA1IqFhBqiBASIFgBqR0DAD1MAAkQJAjUhomAFqYIBIAaBGJDTMADUwQKQAUCMSGmaAGhggUgCoEQkNM0ANDBApANSIhIaZxFB7+X5xfr6/mP3XqHBx0VtFllWLKC18efxQrBKYMI8zhRLiynEiz35zLQRd7Q7d3a3Ev643+57eq0X6qlQ/K5+TgbJhtYbSh3aBCUwk4h5jNwtjiVgKVE5sc9D4H6Wvu41CYkWKBs/D/280JtT2lW4QmIjFAa79SAa1NmmHKaWPtZY6ulbk1FU2o/2pim8LR5sCfk24Oj1M/VS+1T7+vov56Gre+CaZX4lJ6v2v+vHU/d3y8rxVW/l4/HKzFRPd09Lic6cqLKjsKUxgwqKjMRZJBTUf2n08/ixJu7udnVp7+T6/f1vtXtfn/9JaOnz6z3/fiW/DHtAITPhQIkgbbFATE5KgSsxIZ6wGTGjLJ/nS+VV80yxSD54jMBGEEU9GmaBWzV7lgqA2I738e19s9sYJrSH0bP1LrCy2P1s7HkVBYMKTz0M1E+YTcbjV8csCuUHRXLyeNjI6ZO9Za+g6QmBiuGKx1UhmBapZHtosGCUE/dtvJ5+0GtytWsy190sITMRGzaj+pIPap3ELV+7C1uBo/YdBIg1quhbr4BKYGOXXCCslhFrrpafdXa2hdvoDgPqW7JrkOl/StQaaRglMRAjNuC5diGqhPhNhl5UCTFagrHwa6WCBWqSOya9bQC0/n0Y6IqAWqWPy6xZQy8+nkY4o6hWo+HNjpLIF6lbS2wVRoyYcKmhLWt9ATMZoFi/QGL2SZZ+AWpZujXFQQC1Gr2TZJ6CWpVtjHBRQi9ErWfYJqGXp1hgHBdRi9EqWfQJqWbo1xkEBtRi9kmWfgFqWbo1xUFOi1hvDR/nhOb5QO9SPB93EFU2DhcExjjz0ilkT486Jm2sZY/i0m9AFbxHeMNvqL6Fcf9FccDJekHHtAuqXf8ieSoX2vTbTXTrtz91R0zSrRhMaHuNoKtVybncy1Nqi9aPWEY/KGbX+2EOnW1jK7SvTr0XOSEw1tim/1eqfIqYYPiKqgQio8WAK0+Lp66YewshPjCNPHcu5mclRs4rhUwXwud78sAk8NdAbgwNjDWwfxW0VmBw1ixg+H4/fppvSZuuHVfF2P6+FuJX28BArMDlqx/F0x/Cp3p3TTGmVcQG7+BDc3px2O74Vd+VCYHFpCKpG7IrczZGhVhSzy0VRvP3ZNyWVwe8m/kqbrV9rH7uvt4UIQbn6Kl/X2m7t/4hpDyz6pX+i9YZVDB9huy8idtk15xWoZnylzVaIl2EBnSdSLetmp9rs0EcFUuOytGKzt7T2jZrWIrZwKRifCrXjhFWbgvWhytoh9rwP+xBoT3alNwrRsbeDooZ772+mDeLqm9/vEbTWqQDhsgBe4K0AUOPtf8LRAzVCsXmbAmq8/U84eqBGKDZvU0CNt/8JRw/UCMXmbYoXakMvNOjzHvMmZvToeaF2PNFU24+Xp3/r2fSOWgrOREZGPL4U4IVaW7Wu07+HrHpV3mM8XhTgjVrX6d9TmtBLLyKjkVIB1qjpp7QBaULB0AAFGKOmn9Js8x4P0BhFKwWSQ61xT12c4R57GV57oQET2pS/FpkejjINS3v6V/yncpwN90FNQtr/fMKjkfadIC/Zcfq3M+Wi+F3HaUlXL7FEzXSh4SwqZjVXwM71k/tWc/+YILmj5d7N7Fpgh9phObB7muAmfXZ0eB0Q7hZ4lRONdSvAblYDDKEUAGqhlGdnF6ixc3moAQO1UMqzswvU2Lk81IBzW4GGTYws49ng0SqQG2pwc7QK4AUarWty6xhQy82j0Y4HqEXrmtw6BtRy82i04wFq0bomt44Btdw8Gu14gFq0rsmtY0AtN49GOx5uqFUXrmqZWRTH9OcNRc5QJ479nR1PoKVDrG/9lZT+GwcIOO/qXy7XWBqXoTSoVST13Ipq32fBDZeB7HFB7ShLByBqghZVRV01sDaMNW7favqPjZdnEd1qUfxXS/DeuDaPnKFOH2myMlATIlQkFdvfxa/T7+luJRI79qwfPEjPrQmgdvT49eZXLcfy8qn8etv+fPzgRsRk4wVqXdLqc0pO5oj8GwZqwsdGqpAz1MNvAlArRVx+FYFIt88vdUGrpcIxP62mQOPnHjyRfxPDFqzJl+7aoZA7tOeQV639XGzhuvqey76aLp6VPhHuYXbR5Q017QO7OiPv+rjGkv+LK5IR4lstEkfk3w2glr+PIxkhUIvEEfl3A6jl7+NIRgjUInFE/t0Aavn7OJIRArVIHJF/N3iiZrhhIN3ekQxUSQfTfU8hf3iGjZAjajLId/+jTwZaYja/X+xqx9q2N6NzDw3zVPql8/5jiDI6y78syXS0myoZaP2+AY59u9DCa1Y7Zjnuy/AjXpzz+7fV7nWtTwb6/rd1WvL6ap7+nDP5CHihZpazN3fe8oeY7hoHwavMLquH2vFdswmuJYBa3fOmZKCz9etndRD8RgRCLZ/577v9JxK7WP325Ifa6IShNslAxWqhtiwQ72FcdrHCrCrk8qGXbN2O73tDMtDDamFfH7Z6pDJZSabveH6zmv1vWatkOUXVnhtx4lu+K+Xm2f6P2CJZXM7q9Wa3d2K1+vZn72CWSVWgdnT0cXWqSwYqv8bmV4IqzQJUbIxgCWr+fQFqZo2OJWbrh+rjrJYuvlpHNG+Q2rfHreT07+iILNjcMDClOG62obuCENGAY+oK7hZwm1uCjRcv0GDSczMM1Lh5PNh4gVow6bkZBmrcPB5svEAtmPTcDAM1bh4PNl6gFkx6boaBGjePBxsvUAsmPTfDWf21IGzi9qHocEv0nhVqQ52N8pQK4AVKqTZrW0CNtfspBw/UKNVmbQuosXY/5eCBGqXarG0BNdbupxw8UKNUm7UtoMba/ZSDB2qUarO2BdRYu59y8ECNUm3WtoAaa/dTDh6oUarN2hZQY+1+ysEDNUq1WdsCaqzdTzl4oCbU7k5jIHMXnB5dkoJGEWQx6IE3plg1YfoiAz82osbLjqhJtVtJtqu4uLWa7QJhRhSnVZ4BSg++MKQx2G02jWCkkqxamKt2nNOu1PBxOp+2V6xfoIY0Bsu1EiR+drmoByN9eRYRTFdfq4iSh2f5VaTV2D5X8UzxNBVgjdpQGCq2TsFIP/6+t0OTdgcxHWosu/JAzdqlVTqM4vruthF32bo6+4JAzQ4BsUgVUW/F2uEVmVfsFGuVAmo2wlXRlcsFARKv2MilLwPUTNqVm24ig4HIoKdMaMoiQbajy21gssDk50Ct19HyvVnub2jmM81yU7MoZQKSxTBp91bitNaxGya33eoJQdXuYwt3gEOxhav8Op53aDuThjZzFVimsx3gk0yLIjyMxcyPIj4UwLeaDxXRhoUCQM1CJBTxoQBQ86Ei2rBQAKhZiIQiPhQAaj5URBsWCgA1C5FQxIcCQM2HimjDQgGgdhKp+4bBoYh7AQuH5FsEqJ04+iYOb/Q8H4+uBfKlyGpkQK2QV57KU0Idj3sBK1fkXgioFYYbBoWHArlTZDU+oGYlEwq5KwDU3DVEC1YKMEGtWjzWni+PH1byoJA/BZigNlu/Nk6B4TKKP4RsW2KCmq0cKDedAkBtOm3RckMBoAYgqBTI9CD7gGHp7hA0rg+4FxjQm3yL4m4B1e80ezt4gbJHgEoAoEalNHs7QI09AlQCADUqpdnbAWrsEaASgNEKVPwJlEpVKztiW8OqXC6FGKGWi8tSHQdeoKl6Lrl+A7XkXJZqh4Faqp5Lrt9AbYTLGgcttacskQ2oLStQG4haidn8frE7/Fl8vynu5xcN3GTw3FOwyd1qe9MsMNBiNsXzPUkwycg0sUyV/0I2oA7hWQcoHQ6jNmpu4z91JZB5qlQaL1D391M92Q+yAXXqCdQGoYYUUoPkahQGaoO0m60fVsXb/byWYtYYy2OQgYwLA7WBzhVhF0S2ArGoPD7firsyv8HiElnO+qUEagNRE8Wbl0pfbwuRrPGYFhTZgLr1HL4KQ42GAuXysn7rBZsd2OyY4FdESfwjLSAbkF5p7KsNJVCSdHiaOYDOTSEbUFtWnFcb/q2GGqMUwLJglGyoNFwBoDZcM9QYpQBQGyUbKg1XAKgN1ww1RikA1EbJhkrDFQBqwzVDjVEKALVRsqHScAWA2nDNikNWjUYgZ/mPjnDO8qpB7TjIGKOp1wFqYzx4zKpR2xKv/ohwfXfbPt8hOLvZjrGSWR2g5sehL/+KxEGrh7VKmrjTcrO93mzKc0bMH6DmA4CPx59bcbzjx1Jp7OW7SF212r2uL31YSbwNoObBgfop7TCh7Z9UAD1YTLEJoObsNf2UdprQcDj3oDBQ60HNJl2QvFqgfKVhQtOpOvS4Fsq3zuA2DuGWPxWn1ZSDbLgJKoLJAR0HBbSncCvUOp9TgAUHs2lWBWoOfquQ6jqI2578+FJWaYFvtdHLgmo5oNtLG91i3hWB2kj/HpYDO2xl2AqIuwW2SqGcowKY1RwFRHVbBYCarVIo56gAUHMUENVtFQBqtkqhnKMCQM1RQFS3VQCo2SqFco4KADVHAVHdVgGgZqsUyjkqwGsLN7bkeW3nib8VOno02uq8UIvWDRw6hhcoBy9HMUagFoUbOHQCqHHwchRjBGpRuIFDJ4AaBy9HMUagFoUbOHQCqHHwchRjBGpRuIFDJ4CavZerG8jdkav602wjxTYu59lezjukxtDfsOu/pof8LKXIQM2Mmim1SkVSzyVPZJ2qNAZqZtSOJTqiIaj5zNQGkWJbKoJvNftvNX3Jl2dx8XhR/Ce+405PPU4pUmwfdANqjqhVJBXb38Wv02y2W4k8yNwj37ZlBWqOqFXVrze/aqFJl0/l19v25+OHj7azaQOoTeFKba7jKQyl1CZQc/SWkSqk2Ma3miNjx+rLryL01fb5pd5ctVQ4pnPXFGj83FM/4m/Gfq3PvmRX6Ee5Q3uOs9baz8UWLvbV7H57dEEg1QB+xjTbpn1gu66kXArXWOJ/8WTSQywLMnFk/MMAavH7KJMeArVMHBn/MIBa/D7KpIdALRNHxj8MoBa/jzLpIVDLxJHxDwOoufvIcOdAGujIqa1kTMs55zZQc0VN5srof/Q5tUvM5veLXe2g2/amK/27azcjqJ/ynzoC993yb00yq7vMqV2/gcDtIDhmtfG/7ssnyXpfojzx4uzNqf3+t3V+8vpqPr5PEdcEalM6pzcF7fKHmO4aR8OrBGlKFtspu0fbNlCbTm9TTu3Z+vWzOhp+c7j/Mv99t//MNj8aUOtHzSantrYFm5zaYrVQWxaI93De118Cf1rnYL7j+96QU/uwWtjXFVAPWeagzmkMmNUme4GWU1TtuRFnwOW7Um6e7f+ILZLF5axuf3Z7J1arb3/2k3UqYMNAbRrxj6vT87x0nvvk19j8SlClWYCKjZE8l6BAbRrUzK3O1g/Vx1ntJny1jmjeKTW3k06JrD4HaAdjc+dAN6vVe9lsQ72xQDueia3hbkE6s0LiPcULNHEHptN9oJaOrxLvKV6gpQPjT3MmMRNfU+nyBtTS9V1iPccLNDGHpdtdoJau7xLrOVBLzGHpdheopeu7xHoO1BJzWLrdBWp+fdd9e6qRjkWf1SXzjC0T/+GLV/OdGVvU6H7t7C35h/tDigw/vwyG21O7zaZxBrI66F0LNCmvwjQyunTFqPTT3wCt4AXq5wVquD21XNeCzZcWlWDMmuC4uhi7fvoaqBWgFkb4iq3TGUgWGVuAWgjUqlt4xfXdbeO4d4ieENoEaoRiS1NikSoO24oPs1flpUreE1qDQI1Wb3nbvVwQZHvfs0tQoEaIWrnpJi5OiYWmMqGxyNgC1KhQk+/N8vaAZj5jkbElwAZLziZ70tP2ZkKWG23nnbX+DN1JKogtXD9u67891RmrqHlFyjKKlp8ek7eCU7hUL1D2dvCtxh4BKgGAGpXS7O0ANfYIUAkA1KiUZm8HqLFHgEoAoEalNHs7QI09AlQCALUplDbmZ3EvMEW3p20TqPnX15ifxb2A/05P3yJQ86mxvPJUnhLqeNwL+OwubVtAzafexvws7gV8dpe2LaBGqzdja0CNsfNphw7U+vUenY2F1o0pWANq/V4q80DVH2ZXT3wiDNR8qom2ehQAasCDSAGgRiQ0zOBugc8z9sb8LO4FfHaXti3cLcB0Q6QAXqBEQsMMUAMDRAoANSKhYQaogQEiBYAakdAwA9TAAJECQI1IaJjBvpoTA2GzO6aVsxGoOaGGyvYK4AVqrxVKOikA1JzkQ2V7BYCavVYo6aQAUHOSD5XtFQBq9lqhpJMCQM1JPlS2VwCo2WuFkk4KADUn+VDZXgGgZq8VSjopANSc5ENlewWAmr1WE5VsXKD/8vjRNpNHTnegNhFAds2WmM3vF7vD3aX9prifXzRwkynQTqm2d6vtTbOAnaEYStFe0IK1hgKajFTKf2WU0x33QAPSr8191vhPXYmOjGkBx2FnGi/QGF4t9T7Mr0QKvfe/1SdbVjndgVpA1OpUBewGkWmgRiS0zsxs/bAq3u7n319OPzVGZA7YXUfTQM1RQLfqIjauyDkrFpXH51txtxJNLi5nbg1HWBuohXZKM1jg623xLpIdf11W3corp7vd6gGliBQol5f11MfY7CASnpcZJX27HHw+Od2xrxYWZ0nS4Wlmcj93LI+c7ricF/pbjY19LAvYuDr0QIFaaA+wsQ/U2Lg69ECBWmgPsLEP1Ni4OvRAgVpoD7CxD9TYuDr0QIFaaA+wsQ/U2Lg69ECBWmgPsLEP1Ni4OvRAgVpoD7CxD9TYuDr0QIFaaA+wsQ/U2Lg69ECBWmgPsLEP1Ni4OvRAgVpoD7Cx/z/NZIaNxCzq3wAAAABJRU5ErkJggg==)
We divide now 9 by 37 what we write down as 9/37 and we get 0.24324324324324…….
Here we can see 243 in being repeated again and again so we can 243 is in recursion
∴ ![](data:image/png;base64,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)
Note: “A important note in every example except 4 we get solution recursive that is because when we divide it the remainder never becomes zero as in example 4 and remember the numbers which are repeated again and again should be given
symbol above them.”
Question 2.Write the following rational numbers in decimal form.
18/42
Answer:![](data:image/jpeg;base64,/9j/4AAQSkZJRgABAQEAYABgAAD/2wBDAAoHBwgHBgoICAgLCgoLDhgQDg0NDh0VFhEYIx8lJCIfIiEmKzcvJik0KSEiMEExNDk7Pj4+JS5ESUM8SDc9Pjv/2wBDAQoLCw4NDhwQEBw7KCIoOzs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozv/wAARCAHmALMDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIhMUEGE1FhByJxFDKBkaEII0KxwRVS0fAkM2JyggkKFhcYGRolJicoKSo0NTY3ODk6Q0RFRkdISUpTVFVWV1hZWmNkZWZnaGlqc3R1dnd4eXqDhIWGh4iJipKTlJWWl5iZmqKjpKWmp6ipqrKztLW2t7i5usLDxMXGx8jJytLT1NXW19jZ2uHi4+Tl5ufo6erx8vP09fb3+Pn6/8QAHwEAAwEBAQEBAQEBAQAAAAAAAAECAwQFBgcICQoL/8QAtREAAgECBAQDBAcFBAQAAQJ3AAECAxEEBSExBhJBUQdhcRMiMoEIFEKRobHBCSMzUvAVYnLRChYkNOEl8RcYGRomJygpKjU2Nzg5OkNERUZHSElKU1RVVldYWVpjZGVmZ2hpanN0dXZ3eHl6goOEhYaHiImKkpOUlZaXmJmaoqOkpaanqKmqsrO0tba3uLm6wsPExcbHyMnK0tPU1dbX2Nna4uPk5ebn6Onq8vP09fb3+Pn6/9oADAMBAAIRAxEAPwD2aiiigAoopKAOen8Z2UIurhbG+m0+zlMVxqESIYY2Bw3BYOwU9SqkDB9DXQIyuiujBlYZBB4IrgNJurey+Euqw3TKklot5b3CN1Epd8KR6tuXHruHrXVaJLHp2i6Np19cRQ3r2iIkMkgDuyoNwUHk474oW33fiD3+/wDAXxJ4l07wtpjX+otIV5CRRLukkIGSFHsASTwABUl7rKWdpbTR2V3eSXRURQW0YLnIzkkkKoA6liB+lcP4qTUjo/iTUdU0O+kne1mgt5hJbmC1g5xtHm78tgMx256DGBXWL4gt9K8MWd5f29xBJJGscNphXnmfGFVFViGJ6jnp1xg4S2fy/G4Pf7/0LGn+Iba+lvLeaCewubFQ9xBdBQyIRkPlWZSpweQTjBziqS+NLT7PBfSabqEOl3DqseoyJGIiGOFYrv8AMVScAEoOozgc1W07TtQtLXWfEmtWqz6je2//ACD4m3LFEikrDn+Jjk7j0yeOOvMvayWHw90vVLXVjqFl5sEo0h2DQSkuMQxt/rMqcYDOwyuCuOBS318vx/r7wf8AmdzqHiMWWtJpEGl31/dPb/aMW5iAVN23kySLzmrH9p3f9nm6/sK/Eu/b9l32/mY/vZ83Zj/gWfaq97omj6tqZu5nmS+ghEbtbX0sDpGSWAby3HBIJ59KoeC9Umm8O3Vxe3zXVra3U0dvezYzNAhwHYjhuh+bvjNT01/rX+vxD0/rQt2/icy67b6PcaJqNncXETyqZWgZQi4yTslYgZIA45JqRvFejjxHB4fiulnv5g5ZIWVvJ2DJD8/KfQdaoeDUl1M3fiq7QrLqhAtUYcxWq58sfVslz/vD0pNc/wCSheFv+ud7/wCgJVW1SYvQ6O8vLews5by7mWGCFC8kjnAUDqay9K8U2Gr6BLrUMV1HbRNIrJJCfMyhIOEGTnI4HX2qhr8Oo3evWyzaPeX+k2qrMkVs8AE0+TgyeZIpwmAQAMEnJ6Cqfw/1EReHtTmvbeSxt4NQupHmuHjCAGViwyGONvfOB6E1K6+n6ob6GzbeJ0kv7SzvtK1DTJL0H7MbsRkSEDJX5Hba2OcNjoa3K5Kyiu/FmvWmuTxPa6Pp5Z9PikXbJdOV2+cwP3UwTtHU5yccCutqgCiiikAUUUUAFFFFABRVLV9Y07QdOk1DVLpLa2jxudsnk9AAOSfYU2/1vT9NtIbq6nKpcMqwqkbSPKTyAqKCzHHOAOlAFG58S3Fvqo04eHNUlldZJImR7bbIiMqswzMMDLpwcHnpwcP/ALd1H/oU9X/7+2n/AMfqjb6zYav44sVs5XMlvp92s0UsTxSRkyWpG5HAYZHIJHPauooA5iVop9QTUZvh/dyXqEFbl0sTIuOmGM2Rip5dQnnuYbmbwVqUk9vnyZXayLR5GDtPn5GRwcVs3t7badZTXt5MsNvAheSRuiqOppFv7RtPXUDOiWjRCbznOxQhGdxzjAx60AZNxqt3dW8lvc+DdUmhkUq8cj2bKwPUEGfBFV76RNTijh1DwDeXccX+rSdbGQJ24Bm4q/Z+KdIvrqG2imnSS4BMH2i0lhWbAz8jOoD8c8E8c9KivPFMNveXdta6bf6ibFQbt7REKw5G7B3OpZsc4UMeR6ihgUrBbfSpmm034eXNlKy7We3jsY2I9CVmHFEQt4NQbUYfh7cx3rMWNykdiJCT1O4TZycnNdFY3ttqVjDe2comt7hBJHIvRlPQ1PT1TF0OVv0ttVnE+o/Du5vJQu0SXEdjIwHpkzHjk1al1Gee0azm8FalJbMmwwu1kUK+m0z4x7V0FFIZiLrV+ihV8I6sqqMACSzAA/7/ANZdzZadeXD3N18NJJ55DueWWCwZmPqSZsmuvooAxBreoKAq+EtXAAwAJbPj/wAj1WNyWs5bM+BL420zFpYCLLY5JySV87BJPJrpKKAOPgsNNtZ0uLf4ZvDNGwZJI4NPVlI6EETcGtmHWb+WeON/DGqQq7BTI8lqVQE9TtmJwOvAJ9q16KACiiigAooooAKKKKAPMPF94upaZr15qtrqCPb288GnW5064McXBUytJs2bm7HOFU9eTXbW2saba+GLfV7yQ29tDAMyXELxsvGOFYBsk8DjnjGcitG/sbbU7CewvI/Nt7hDHKm4ruU8EZHI/Cqep+HNL1iK0ivYZWWycPbmK4kiaNgMAgowOcULRW9P1/zB6u/r+hyugwahdfEdfEOoWpsv7S0ydLe0cfvI4o5INpf0Zt5JXtwK76uftvDw0/xVaX1qbyS3WyuIpXub6WfazPCVAEjsRkI/T0Ge1dBRp0C7e5z/AI406xvvCOqPeWdvcNb2U0kLTRK5jbYfmXI4PuKztXezT4Sj7fFLLbvpsKMkTbWJZVC4Yg45I5wceh6V0WraNZ63bfZr77Q0JBDJDdSwhwRghtjDcMdjkU2z0LTrLTX02OGSazddrQ3U73C7cY2/vC2Fx26UujXe36jvqn2v+n+Ryeoxazpt14a/4SK5t9TtEvY0DW0RilS4KlY2bkiRRk52hOxwelaHha4hsLvxVHeSLC8GpSXMu84xEyKVc+2AefY+lath4V0fTp4JoIJna2XbALi6lnWEYx8iuxCccZAHHHSrV9omk6nNHNqGl2d3LEMRvPbpIyd+CRxTfX5/jb/In/gfr/mZHw8ikh8C6YJEKb0aRVYYIVnZl4+hFdLRRTbuxhRRRSAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiq19dTWlv5kFhcXz7seVbtGG+vzsox+NAFmiq9lcy3duJZrGeyfJHlTtGWHv8AIzD9a5XVLSaD4m+Hp31C6nSaO72wSbBHDhF+6FUHv1Yk0dbB0OyorjvE019qXiyy0CCzju7UWb3c8E1wYYpjuCqshCsSo+Y7cEEkZ4FV5r2GHwv4h0m0t7TwtfWMe6Q2xHkrvHySKyKCdwGPuhgegPGVfS47a2O5orza1S1tNW8N7PDx8LXUsv725KoFul2HMJdMlmY7TiUKflJHzcV6TVWJuFFFFIYUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFZl5qt7bXTww+HtRu0XGJoZLYI3GeN8qtx05A6UAadc3qfh7Wr7xDZ6tDrFjD9g80W8T6e78SAA7j5wyeOMAVa/t3Uf+hT1f8A7+2n/wAfo/t3Uf8AoU9X/wC/tp/8fo63AXVNCmu9RtNWsb1bPUbWNohI8PmRyRtgsrpuBIyARhhg+tVD4NgvLLVE1W7e5utWKfaJ4kEQTZ/qxGpLbQvXktk5J9Ktf27qP/Qp6v8A9/bT/wCP0f27qP8A0Ker/wDf20/+P0AV/wDhHNSv5bEa7q8F7BYyrPGkFn5DSSr91nJds45OFC8+3FdFWL/buo/9Cnq//f20/wDj9H9u6j/0Ker/APf20/8Aj9AG1RWZZ6re3N0kM3h7UbRGzmaaS2KLxnnZKze3APWtOgAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiorm3S7t3t5GkVHGCYpWjYfRlII/A0AENzBc+Z5E0cvlOY32OG2sOqnHQj0qo2v6Kmo/2a+r2K3u4L9mNygl3HoNuc5rB+HdtFZ6frNtCGEUWs3SIGcscBh1JJJ+pOah8YpZ/2TJ4Q0ezik1HVssIY1GIQWBa4kI6AHkE8lsAZo7edg7+V/wOsvtQstMt/tOoXkFpACF8yeVY1yegyTinWt3bX1slzaXEVxBIMpLE4dWHsRwa5mSPzPiVp1vcN5os9Iklh3f89C6oz/Xbx+J9af4cAt/GXim0hwtuJYJ9g6CR4/nP1OAT+dC/z/B2EdTRRRQMKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAqK5hee3eKO4ktnYYEsQUsnuNwI/MGpaKAMTQvDX9gzXDxavf3SXMrzyxXAh2mRyCzfLGpB46Zx7VVtPBzafc3dxZ+I9WilvJTLM5W2dmPYbmhLYA4AzgDpXS1z2ta7dW/iGw0KyktbWa9ieVbm8Quh2kDy0QMu5znP3hgDvR1X9f1sBbv/D8V+9ncG9uoL6yUrFewlBIQwAYMCpQg4BIK4yMjFTaRo1vo8c/lSSzz3MpmuLidgZJnPGTgADAAAAAAA4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)
= 0.428571428571428571…
So, as we can see 428751 repeats itself so we can write it as ![](data:image/png;base64,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)
∴![](data:image/png;base64,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)
Note: “A important note in every example except 4 we get solution recursive that is because when we divide it the remainder never becomes zero as in example 4 and remember the numbers which are repeated again and again should be given
symbol above them.”
Question 3.Write the following rational numbers in decimal form.
9/14
Answer:![](data:image/jpeg;base64,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htNXs4uLa01e4it0HREyDtHsCx+lJa/n/X3jen9eVy/wDavFX/AEBtI/8ABrL/API9H2rxV/0BtI/8Gsv/AMj1tUUAQWb3T2qNewww3BzvjhlMqDnjDFVJ4x2H9anoooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAqtfWst3bGKG+nsmJB82BYy30+dWH6UUUbgZ2g+G18P6WdNt9VvprYIUiWbysw5JJKlUBzk/wAWaqaX4OfRrf7PY+JNWjjLmR8pas0jE5LMxh3MT6k5ooovrcC9f+H47vUhqdtfXenXvleS81qYyZUzkBldWU4OcHGRk81a0nSbXRdPSxs1YRqSzM7FnkYnLMxPUkkk0UUAXaKKKACiiigAooooA//Z)
cannot be further reduced so we have to divide it and we get 0.64285714285714… . As we can see 428571 is recursive so we can write it as
. It is important to note that 6 is not recurring so there is no
symbol above it.
∴
.
Note: “A important note in every example except 4 we get solution recursive that is because when we divide it the remainder never becomes zero as in example 4 and remember the numbers which are repeated again and again should be given
symbol above them.”
Question 4.Write the following rational numbers in decimal form.
-103/5
Answer:![](data:image/jpeg;base64,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)
The above solution is for
when we multiply the quotient by negative (-) sign. We get the solution for
.
∴ ![](data:image/png;base64,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)
Note: “A important note in every example except 4 we get solution recursive that is because when we divide it the remainder never becomes zero as in example 4 and remember the numbers which are repeated again and again should be given
symbol above them.”
Question 5.Write the following rational numbers in decimal form.
-11/13
Answer:![](data:image/jpeg;base64,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)
we get 0.8461538461538… . As we can see 846153 is recursive so we can write it as ![](data:image/png;base64,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)
∴ ![](data:image/png;base64,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)
Note: “A important note in every example except 4 we get solution recursive that is because when we divide it the remainder never becomes zero as in example 4 and remember the numbers which are repeated again and again should be given
symbol above them.”
Write the following rational numbers in decimal form.
9/37
Answer:
We divide now 9 by 37 what we write down as 9/37 and we get 0.24324324324324…….
Here we can see 243 in being repeated again and again so we can 243 is in recursion
∴
Note: “A important note in every example except 4 we get solution recursive that is because when we divide it the remainder never becomes zero as in example 4 and remember the numbers which are repeated again and again should be given symbol above them.”
Question 2.
Write the following rational numbers in decimal form.
18/42
Answer:
= 0.428571428571428571…
So, as we can see 428751 repeats itself so we can write it as
∴
Note: “A important note in every example except 4 we get solution recursive that is because when we divide it the remainder never becomes zero as in example 4 and remember the numbers which are repeated again and again should be given symbol above them.”
Question 3.
Write the following rational numbers in decimal form.
9/14
Answer:
cannot be further reduced so we have to divide it and we get 0.64285714285714… . As we can see 428571 is recursive so we can write it as
. It is important to note that 6 is not recurring so there is no
symbol above it.
∴.
Note: “A important note in every example except 4 we get solution recursive that is because when we divide it the remainder never becomes zero as in example 4 and remember the numbers which are repeated again and again should be given symbol above them.”
Question 4.
Write the following rational numbers in decimal form.
-103/5
Answer:
The above solution is for when we multiply the quotient by negative (-) sign. We get the solution for
.
∴
Note: “A important note in every example except 4 we get solution recursive that is because when we divide it the remainder never becomes zero as in example 4 and remember the numbers which are repeated again and again should be given symbol above them.”
Question 5.
Write the following rational numbers in decimal form.
-11/13
Answer:
we get 0.8461538461538… . As we can see 846153 is recursive so we can write it as
∴
Note: “A important note in every example except 4 we get solution recursive that is because when we divide it the remainder never becomes zero as in example 4 and remember the numbers which are repeated again and again should be given symbol above them.”
Practice Set 1.4
Question 1.The number √2 is shown on a number line. Steps are given to show √3 on the number line using √2. Fill in the boxes properly and complete the activity.
Activity :
● The point Q on the number line shows the number.......
● A line perpendicular to the number line is drawn through the point Q.
Point R is at unit distance from Q on the line.
![](data:image/png;base64,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)
● Right angled ∆ORQ is obtained by drawing seg OR.
● l(OQ) = √2, l(QR) = 1
∴ by Pythagoras theorem,
[l(OR)]2= [l(OQ)]2+ [l(QR)]2
=
2+
2=
+![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACEAAAAlCAYAAADMdYB5AAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAACaSURBVFjDY2hsbGQYaDzgDkBxREdHB0d5ebkErS0sLi5WwOkIdXX1DQwMDP/pgV1cXEqwOiIwMDDBwMBgPq1DQkBA4D56aIw6YtQRo44YdcSoI0YdMeqIUUeMOmLUEaOOGHXEqCNGpiOsrKw6xMXFzzs4ODTQErOzs7+Pjo72wuoINze3AhkZmeO0dgQoJJKSkmwH7yDJiHcEAB2f/MZRmAEHAAAAAElFTkSuQmCC)
=
∴ l(OR) =![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACEAAAAlCAYAAADMdYB5AAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAACaSURBVFjDY2hsbGQYaDzgDkBxREdHB0d5ebkErS0sLi5WwOkIdXX1DQwMDP/pgV1cXEqwOiIwMDDBwMBgPq1DQkBA4D56aIw6YtQRo44YdcSoI0YdMeqIUUeMOmLUEaOOGHXEqCNGpiOsrKw6xMXFzzs4ODTQErOzs7+Pjo72wuoINze3AhkZmeO0dgQoJJKSkmwH7yDJiHcEAB2f/MZRmAEHAAAAAElFTkSuQmCC)
Draw an arc with center O and radius OR. Mark the point of intersection of the line and the arc as C. The point C shows the number √3.
Answer:Activity :
● The point Q on the number line shows the number ...
... .
● A line perpendicular to the number line is drawn through the point Q.
Point R is at unit distance from Q on the line. (Here unit distance means 1 cm or any other unit that you choose earlier)
![](data:image/png;base64,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)
● Right angled ∆ORQ is obtained by drawing seg OR.
● l(OQ) = √2, l(QR) = 1
∴ by Pythagoras theorem,
[l(OR)]2= [l(OQ)]2+ [l(QR)]2
![](data:image/png;base64,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)
= 3 ∴ l(OR) =![](data:image/png;base64,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)
The solution for drawing
:
To represent √3 on the number line, first of all, we have to represent √2 on the number line. The procedure for the representation of √2 will be same as shown in the activity. So, let’s start from there only. The steps further followed will be as:
Step I: Now we need to construct a line which is perpendicular to line AB from point A such that this new line has unity length and let’s name the new line as AE.
Step II: Now join (C) and (E). The length of line CE could be found out by using Pythagoras theorem in right angled triangle EAC. So;
AE2+ AC2= EC2
⟹ EC2= 12+ (√2)2
⟹ EC2= 1 + 2
⟹ EC2= 3
⟹ EC = √3
So the length of EC line is found to be √3 units.
Step III: Now, with (C) as center and EC as the radius of circle cut an arc on the number line and mark the point as F. Since, OE is the radius of the arc, hence OF will also be the radius of the arc and will have the same length as that of OE. So, OF = √3 units. Hence, F will represent √3 on the number line.
Similarly, we can represent any rational number on the number line. The positive rational numbers will be represented on the right of (C) and the negative rational numbers will be on the left of (C). If m is a rational number greater than the rational number y then on the number line the point representing x will be on the right of the point represents.
Question 2.Represent √5 on the number line.
Answer:Steps involved are as follows:
Step I: Draw a number line and mark the center point as zero.
Step II: Mark right side of the zero as (1) and the left side as (-1).
Step III: We won’t be considering (-1) for our purpose.
Step IV: With 2 units as length draw a line from (1) such that it is perpendicular to the line.
Step V: Now join the point (0) and the end of the new line of 2 units length.
Step VI: A right-angled triangle is constructed.
Step VII: Now let us name the triangle as ABC such that AB is the height (perpendicular), BC is the base of triangle and AC is the hypotenuse of the right-angled ΔABC.
Step VIII: Now the length of the hypotenuse, i.e., AC can be found by applying Pythagoras theorem to the triangle ABC.
AC2= AB2+ BC2
⟹ AC2= 22+ 12
⟹ AC2= 4 + 1
⟹ AC2= 5
⟹ AC= √5
Step IX: Now with AC as radius and C as the center cut an arc on the same number line and name the point as D.
Step X: Since AC is the radius of the arc and hence, the CD will also be the radius of the arc whose length is √5.
Step XI: Hence, D is the representation of√5 on the number line.
Question 3.Show the number √7 on the number line.
Answer:Draw a number line l and mark the points O,A and B such that OA = OB = 1. Draw BC perpendicular to number line such that BC = 1 units. Join OC
In Right
OBC,
OC2= OB2+ BC2
= (2)2+ (1)2
= 5
OC =![](data:image/png;base64,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)
Taking O as center and C and C as radius, draw an arc which cuts l in D.
Hence, OC = OD =![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABYAAAAXCAMAAAA4Nk+sAAAAAXNSR0IArs4c6QAAAHhQTFRFAAAAAAAAAAA6AABmADpmADqQAGa2OgAAOjoAOjpmOjqQOmaQOpDbZgAAZgBmZjo6ZjqQZrbbZrb/kDoAkDo6kDpmkGY6kNv/tmYAtmY6ttv/tv//25A625Bm27Zm29u229v/2////7Zm/9uQ/9u2/9vb//+2///b0prn0QAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAArElEQVQoU51Q2xaCIBBcMqObXcSKktKE4P//sIVF45x4cp7WYXcuAsyEYuX7/9Q1t5yePWV2AYZV1lzWI/1M1NylBdCcIRYJrbcorfl0Ek/VHoeU/vT+5e4vf7S5Mh/BHlA6obteFshQPM03nC3JUXOUVcHLNWcwgpI4UbRp87CGGFgd4kXYivo6Ub5oQVJK+gDF1lRDoqxBTaJtFSdzxO67xyin8n9vsps3fAEY4gpZPhvmNAAAAABJRU5ErkJggg==)
Now, draw DE perpendicular number line l such that DE = 1 Units. Join OE.
In Right
,
OE2= OD2+ DE2
= (
)2+ (1)2
=5 + 1
=6
![](data:image/png;base64,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)
Taking O as center and OE as radius, draw an arc which cuts l in F.
![](data:image/png;base64,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)
Now, Draw GF perpendicular l such that GH = 1 units. Join OG.
In right![](data:image/png;base64,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)
OG2= OF2+ GF2
= (
2+ (1)2
= 6 + 1
= 7
OG =![](data:image/png;base64,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)
Taking O as center and OG as radius, Draw an arc which cuts l in H.
Hence,
OG = OH =![](data:image/png;base64,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)
![](data:image/jpeg;base64,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The number √2 is shown on a number line. Steps are given to show √3 on the number line using √2. Fill in the boxes properly and complete the activity.
Activity :
● The point Q on the number line shows the number.......
● A line perpendicular to the number line is drawn through the point Q.
Point R is at unit distance from Q on the line.
● Right angled ∆ORQ is obtained by drawing seg OR.
● l(OQ) = √2, l(QR) = 1
∴ by Pythagoras theorem,
[l(OR)]2= [l(OQ)]2+ [l(QR)]2
=2+
2=
+
= ∴ l(OR) =
Draw an arc with center O and radius OR. Mark the point of intersection of the line and the arc as C. The point C shows the number √3.
Answer:
Activity :
● The point Q on the number line shows the number ...... .
● A line perpendicular to the number line is drawn through the point Q.
Point R is at unit distance from Q on the line. (Here unit distance means 1 cm or any other unit that you choose earlier)
● Right angled ∆ORQ is obtained by drawing seg OR.
● l(OQ) = √2, l(QR) = 1
∴ by Pythagoras theorem,
[l(OR)]2= [l(OQ)]2+ [l(QR)]2
= 3 ∴ l(OR) =
The solution for drawing :
To represent √3 on the number line, first of all, we have to represent √2 on the number line. The procedure for the representation of √2 will be same as shown in the activity. So, let’s start from there only. The steps further followed will be as:
Step I: Now we need to construct a line which is perpendicular to line AB from point A such that this new line has unity length and let’s name the new line as AE.
Step II: Now join (C) and (E). The length of line CE could be found out by using Pythagoras theorem in right angled triangle EAC. So;
AE2+ AC2= EC2
⟹ EC2= 12+ (√2)2
⟹ EC2= 1 + 2
⟹ EC2= 3
⟹ EC = √3
So the length of EC line is found to be √3 units.
Step III: Now, with (C) as center and EC as the radius of circle cut an arc on the number line and mark the point as F. Since, OE is the radius of the arc, hence OF will also be the radius of the arc and will have the same length as that of OE. So, OF = √3 units. Hence, F will represent √3 on the number line.
Similarly, we can represent any rational number on the number line. The positive rational numbers will be represented on the right of (C) and the negative rational numbers will be on the left of (C). If m is a rational number greater than the rational number y then on the number line the point representing x will be on the right of the point represents.
Question 2.
Represent √5 on the number line.
Answer:
Steps involved are as follows:
Step I: Draw a number line and mark the center point as zero.
Step II: Mark right side of the zero as (1) and the left side as (-1).
Step III: We won’t be considering (-1) for our purpose.
Step IV: With 2 units as length draw a line from (1) such that it is perpendicular to the line.
Step V: Now join the point (0) and the end of the new line of 2 units length.
Step VI: A right-angled triangle is constructed.
Step VII: Now let us name the triangle as ABC such that AB is the height (perpendicular), BC is the base of triangle and AC is the hypotenuse of the right-angled ΔABC.
Step VIII: Now the length of the hypotenuse, i.e., AC can be found by applying Pythagoras theorem to the triangle ABC.
AC2= AB2+ BC2
⟹ AC2= 22+ 12
⟹ AC2= 4 + 1
⟹ AC2= 5
⟹ AC= √5
Step IX: Now with AC as radius and C as the center cut an arc on the same number line and name the point as D.
Step X: Since AC is the radius of the arc and hence, the CD will also be the radius of the arc whose length is √5.
Step XI: Hence, D is the representation of√5 on the number line.
Question 3.
Show the number √7 on the number line.
Answer:
Draw a number line l and mark the points O,A and B such that OA = OB = 1. Draw BC perpendicular to number line such that BC = 1 units. Join OC
In Right OBC,
OC2= OB2+ BC2
= (2)2+ (1)2
= 5
OC =
Taking O as center and C and C as radius, draw an arc which cuts l in D.
Hence, OC = OD =
Now, draw DE perpendicular number line l such that DE = 1 Units. Join OE.
In Right ,
OE2= OD2+ DE2
= ()2+ (1)2
=5 + 1
=6
Taking O as center and OE as radius, draw an arc which cuts l in F.
Now, Draw GF perpendicular l such that GH = 1 units. Join OG.
In right
OG2= OF2+ GF2
= (2+ (1)2
= 6 + 1
= 7
OG =
Taking O as center and OG as radius, Draw an arc which cuts l in H.
Hence,
OG = OH =