Write the denominator of the following in the form 2ᵐ x 5ⁿ where ‘n’ and ‘m’ are positive integers. Also write it’s decimal expansion. 23/20

Question

Write the denominator of the following in the form 2ᵐ x 5ⁿ where ‘n’ and ‘m’ are positive integers. Also write it’s decimal expansion. 23/200

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1 week 2021-09-14T05:21:06+00:00 1 Answer 0 views 0

The value of m is 5 and n is 3

Step-by-step explanation:

Given the fraction

\frac{241}{4000}4000241

we have to convert above in the form

\frac{241}{4000}=\frac{241}{2^m\times 5^n}4000241=2m×5n241

To find the value of m and n

The prime factorization of 4000 is

4000=2\times 2\times 2\times 2\times 2\times 5\times 5\times 5=2^5\times 5^34000=2×2×2×2×2×5×5×5=25×53

which is in the form 2^m\times 5^n2m×5n

implies m=5 and n=3

The decimal expansion is

\frac{241}{4000}=\frac{241}{4\times 1000}=\frac{60.25}{1000}=0.060254000241=4×1000241=100060.25=0.06025