**NCERT Solution For Class 10, Maths, Real Numbers, Exercise 1.4 ** includes questions related to rational numbers which will have a terminating decimal expansion or a non-terminating repeating decimal expansion. The detailed explanation of each question is given below.

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Toggle## Class 10, Maths, Chapter 1, Exercise 1.4, Solutions

**Q.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) $\frac{13}{3125}$**

**(ii) $\frac{17}{8}$**

**(iii) $\frac{64}{455}$**

**(iv) $\frac{15}{1600}$**

**(v) $\frac{29}{343}$**

**(vi) $\frac{23}{{{2}^{3}}{{5}^{2}}}$**

**(vii) $\frac{129}{{{2}^{2}}{{5}^{7}}{{7}^{5}}}$**

**(viii) $\frac{6}{15}$**

**(ix) $\frac{35}{50}$**

**(x) $\frac{77}{210}$**

**Ans: **We know that if the denominator of a rational number has no prime factors other than 2 or 5, then it is expressed as a terminating, otherwise it is non- terminating repeating decimal expansion. Thus, we have to check the prime factors of the denominators of each of the given rational numbers.

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

**Ans:**

**Q.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 ** **, what can you say about the prime factors of q? **

**(i) 43.123456789**

**(ii) 0.120120012000120000….**

**(iii) 43. $\overline{123456789}$**

**Ans:**