Question 1 iiWithout actually performing the long division- state whether 17-8 will have a terminating decimal expansion or a non-terminating repeating decimal expansion-

Name: NCERT - Grade 10 - Mathematics - Real Numbers - Q16_2
Uploaded: 2022-07-04T10:36:42+05:30
Description: 17/8 On factorising the denominator, we get: 8 =2 × 2 × 2 = 2^3 Here, denominator is in the form of 2^m× 5^n, where m = 3 and n = 0. It means that rational numb ...

17/8 On factorising the denominator, we get: 8 =2 × 2 × 2 = 2^3 Here, denominator is in the form of 2^m× 5^n, where m = 3 and n = 0. It means that rational numb ...

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Standard IX

Mathematics

Real Numbers

Question 1 ii...

Question

Question 1 (ii)
Without actually performing the long division, state whether $\frac{17}{8}$ will have a terminating decimal expansion or a non-terminating repeating decimal expansion.

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Solution

$\frac{17}{8}$
On factorising the denominator, we get:
$8 = 2 \times 2 \times 2 = 2^{3}$
Here, denominator is in the form of $2^{m} \times 5^{n}$ , where m = 3 and n = 0.
It means that rational number $\frac{17}{8}$ has terminating decimal expansion.

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Question 1 (ii) Without actually performing the long division, state whether 178 will have a terminating decimal expansion or a non-terminating repeating decimal expansion.

178 On factorising the denominator, we get: 8=2×2×2=23 Here, denominator is in the form of 2m×5n, where m = 3 and n = 0. It means that rational number 178 has terminating decimal expansion.

Question 1 (ii)
Without actually performing the long division, state whether $\frac{17}{8}$ will have a terminating decimal expansion or a non-terminating repeating decimal expansion.

$\frac{17}{8}$
On factorising the denominator, we get:
$8 = 2 \times 2 \times 2 = 2^{3}$
Here, denominator is in the form of $2^{m} \times 5^{n}$ , where m = 3 and n = 0.
It means that rational number $\frac{17}{8}$ has terminating decimal expansion.