Ncert Solutions for Class 10 Maths

Exercise 1.4 (Revisiting Rational Numbers and Their Decimal Expansions)

1. Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non-terminating repeating decimal expansion : (i) \(13 \over 3125\) (ii) \(17 \over 8\) (iii) \(64 \over 455\) (iv) \(15 \over 1600\) (v) \(29 \over 343\) (vi) \(23 \over 2^3 5^2\) (vii) \(129 \over 2^2 5^7 7^5\) (viii) \(6 \over 15\) (ix) \(35 \over 50\) (x) \(77 \over 210\)

2. Write down the decimal expansions of those rational numbers in Question 1 above which have terminating decimal expansions.

3. The following real numbers have decimal expansions as given below. In each case, decide whether they are rational or not. If they are rational, and of the form \(p \over q\), what can you say about the prime factors of q? (i) 43.123456789 (ii) 0.120120012000120000. . . (iii) \(43.\overline{123456789}\).

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