If is expressed as a terminating decimal, how many non zero digits will d have?

Foundation

Mathematics Foundation

Properties of Real Number

Recurring Decimal Number

Linear Equations in One Variable

Question

If $d = \frac{1}{2^{3} \times 5^{7}}$ is expressed as a terminating decimal, how many non zero digits will d have?

Three

Seven

Ten

Two

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Given,

d = \frac{1}{2^{3} \times 5^{7}}

Multiply and divide by 2⁴,

\Rightarrow d = \frac{2^{4}}{2^{3} \times 5^{7} \times 2^{4}}

\frac{16}{2^{7} \times 5^{7}}

\frac{16}{10^{7}}

= 0.0000016

Hence, d will have two non-zero digits, 1 and 6, when expressed as a decimal.

Therefore, option B is the correct answer.