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

[(i) 13/3125 (ii) 17/8 (iii) 64/455 (iv) 15/1600 (v)29/343 (vi) 23/2^{3}5^{2 }(vii) 129/2^{2}5^{7}7^{5 }(viii) 6/15

(ix) 35/50 (x) 77/210]

**Solution:**

The terminating decimal expansion means that the decimal representation or expansion terminates after a certain number of digits. A rational number is terminating if it can be expressed in the form: p / q where q is of the form 2^{n }× 5^{m}.

The rational numbers 13/3125, 17/8, 15/1600, 23/2^{3}5^{2}, 6/15, and 35/50 have a terminating decimal expansion whereas, 64/455, 29/343, 129/2^{2}5^{7}7^{5,} and 77/210 have a non-terminating repeating decimal expansion.

(i) 13/3125 = 0*.*00416

(ii) 17/8 = 2.125

(iv) 15/1600 = 0*.*009375

(vi) 23/ (2^{3} × 5^{2}) = 23/200 = 0*.*115

(viii) 6/15 = (2 × 3)/(3 × 5) = 2/5 = 0.4

(ix) 35/50 = 0.7

**☛ Check: **NCERT Solutions for Class 10 Maths Chapter 1

**Video Solution:**

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

NCERT Solutions Class 10 Maths Chapter 1 Exercise 1.4 Question 2

**Summary:**

The terminating decimal expansion of the rational numbers 13/3125, 17/8, 15/1600, 23/2^{3}5^{2}, 6/15 and 35/50 are 0.00416, 2.125, 0.009375, 0.115, 0.4 and 0.7 respectively.

**☛ Related Questions:**

- Prove that 3 + 2√5 is irrational.
- Prove that the following are irrationals: (i) 1/√2 (ii) 7√5 (iii) 6 + √2
- 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) 13/3125 (ii) 17/8 (iii) 64/455 (iv) 15/1600 (v) 29/343 (vi) 23/2352 (vii) 129/225775 (viii) 6/15 (ix) 35/50 (x) 77/210
- 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/q, what can you say about the prime factor of q? (i) 43.123456789 (ii) 0.120120012000120000.... (iii) 43.123456789

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