NCERT Solutions for Class 9 Math | Exercise 1.3

Chapter 1 of CBSE NCERT Class 9 Math covers number system. Concepts covered in exercise 1.3 include rational numbers, decimal expansion of rational numbers, terminating decimals - also known as finite decimals, non-terminating decimals - also known as infinite decimals, recurring decimals also known as repeating decimals, fractional equivalents of non-terminating recurring decimals.

Solutions to Question 1, Question 7, Question 8, and Question 9 are given in this page. For the other questions, click on the solution links given adjacent to the questions.

NCERT Solutions for Class 9 Math | Exercise 1.3

1. Question 1

   Write the following in decimal form and say what kind of decimal expansion each has:
   i) \\frac{36}{100})
   ii) \\frac{1}{11})
   iii) 4\\frac{1}{8})
   iv) \\frac{3}{13})
   v) \\frac{2}{11})
   vi) \\frac{329}{400})

   Answer

   i) \\frac{36}{100}) = 0.36. It is a terminating decimal.
   ii) \\frac{1}{11})= 0.\\overline{09}). It is a non-terminating repeating decimal expansion.
   iii) 4\\frac{1}{8}) = 4.125. It is a terminating decimal.
   iv) \\frac{3}{13}) = 0.\\overline{230769}). It is a non-terminating repeating decimal expansion.
   v) \\frac{2}{11}) = 0.\\overline{18}). It is a non-terminating repeating decimal expansion.
   vi) \\frac{329}{400}) = 0.8225. It is a terminating decimal.

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2. Question 2

   You know that the value of \\frac{1}{7}) = 0.\\overline{142857}). Can you predict what the decimal expansions of \\frac{2}{7}), \\frac{3}{7}), \\frac{4}{7}), \\frac{5}{7}), and \\frac{6}{7}) are, without doing the long division? If so, how?

   Solution

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3. Question 3

   Express the following in the form \\frac{p}{q}), where p and q are integers and q ≠ 0:
   i) 0.\\overline{6})
   ii) 0.4\\overline{7})
   iii) 0.\\overline{001})

   Solution

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4. Question 4

   Express 0.\\overline{9}) in the form \\frac{p}{q}):

   Solution

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5. Question 5

   What can the maximum number of digits be in the repeating block of digits in the decimal expansion of \\frac{1}{17})? Perform the division to check.

   Solution

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6. Question 6

   Look at several examples of rational numbers in the form \\frac{p}{q}) (q ≠ 0), where p and q are integers with no common factors other than 1 and have terminating decimal expansions. What property must q satisfy?

   Solution

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7. Question 7

   Write three numbers whose decimal expansions are non-terminating non-recurring.

   Answer
   1. 0.1401400140001400001400000...
   2. 0.080080008000080000080000008...
   3. 0.40400400040000400000...

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8. Question 8

   Find three different irrational numbers between the rational numbers \\frac{5}{7}) and \\frac{9}{11}).

   Answer

   First, let us find the decimal expansions of \\frac{5}{7}) and \\frac{9}{11}).
   \\frac{5}{7} = 0.\overline{714285})
   \\frac{9}{11} = 0.\overline{81})
   We have to find irrational numbers between 0.\\overline{714285}) and 0.\\overline{81})

   If we write three numbers that are non-terminating and non-recurring, we will have written three irrational numbers between the two given fractions.
   0.73073007300073..., 0.7890789007890007890000..., and 0.80800800080000... are irrational numbers between the two given fractions.

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9. Question 9

   Classify the following numbers as rational or irrational:
   i) √23
   ii) √225
   iii) 0.3769
   iv) 7.478478....
   v) 1.101001000100001...

   Answer

   i) √23 = 4.753... It is a non-terminating and non-recurring decimal. It is an irrational number. It cannot be expressed in the form \\frac{p}{q}) where p and q are integers and q ≠ 0.

   ii) √225 = 15. It is a terminating decimal. It is a rational number. It can be expressed in the form \\frac{p}{q}) as \\frac{15}{1}).

   iii) 0.3769. It is a terminating decimal. It is a rational number. It can be expressed in the form \\frac{p}{q}) as \\frac{3769}{10000}).

   iv) 7.478478.... It is a non-terminating but recurring decimal. It is a rational number. It can be expressed in the form \\frac{p}{q}) as 7\\frac{478}{999}) or \\frac{7471}{999}).

   v) 1.101001000100001... It is a non-terminating and non-recurring decimal. It is an irrational number. It cannot be expressed in the form \\frac{p}{q}) where p and q are integers and q ≠ 0.