If 0-2317 is expressed in the form of pq- where -p- and -q- are co-prime and also -q- is in the form 2n- 5m- what are the values of -m- and -n- respectively-

The correct option is C 4, 4 0.2317=0. 2317×10000 1× 10000 =231710000 2317 and 10000 are co prime numbers. 231710000= 2317 2 ^ 4 × ...

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Byju's Answer

Standard VII

Mathematics

Writing Rational Numbers as Decimals

If 0.2317 i...

Question

If $0.2317$ is expressed in the form of $\frac{p}{q}$ , where 'p' and 'q' are co-prime and also 'q' is in the form $2^{n} \times 5^{m}$ , what are the values of 'm' and 'n' respectively?

4, 3

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4, 5

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4, 4

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3, 4

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Solution

The correct option is C $4, 4$
$0.2317 = \frac{0. 2317 \times 10000}{1 \times 10000} = \frac{2317}{10000}$
$2317$ and $10000$ are co-prime numbers.
$\frac{2317}{10000} = \frac{2317}{2^{4} \times 5^{4}}$
$∴ n = 4, m = 4$
Hence, the correct answer will be option C.

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If 0.2317 is expressed in the form of pq, where 'p' and 'q' are co-prime and also 'q' is in the form 2n×5m, what are the values of 'm' and 'n' respectively?

The correct option is C 4,40.2317=0.2317×100001×10000=2317100002317 and 10000 are co-prime numbers.231710000=231724×54∴n=4,m=4Hence, the correct answer will be option C.

If $0.2317$ is expressed in the form of $\frac{p}{q}$ , where 'p' and 'q' are co-prime and also 'q' is in the form $2^{n} \times 5^{m}$ , what are the values of 'm' and 'n' respectively?

The correct option is C $4, 4$
$0.2317 = \frac{0. 2317 \times 10000}{1 \times 10000} = \frac{2317}{10000}$
$2317$ and $10000$ are co-prime numbers.
$\frac{2317}{10000} = \frac{2317}{2^{4} \times 5^{4}}$
$∴ n = 4, m = 4$
Hence, the correct answer will be option C.