Question

In the form of \( \frac{p}{2^n \times 5^m} \), \( 0.105 \) can be written as

• A. \( \frac{21}{2^2 \times 5^2} \)
• B. \( \frac{21}{2^3 \times 5^3} \)
• C. \( \frac{21}{2^3 \times 5^2} \)
• D. \( \frac{21}{2 \times 5^3} \)

Hint:

When converting decimals to fractions, simplify by factoring the denominator.

Answer 1

The Correct Option is C

Step 1: Express \( 0.105 \) as a fraction: \[ 0.105 = \frac{105}{1000} \] Step 2: Simplify the fraction: \[ \frac{105}{1000} = \frac{21}{200} \] Step 3: Express \( 200 \) as \( 2^3 \times 5^2 \): \[ \frac{21}{200} = \frac{21}{2^3 \times 5^2} \] Thus, the correct answer is \( \frac{21}{2^3 \times 5^2} \).