Question

The decimal expansion of number \(\dfrac{441}{2^2\times5^3\times7}\) _______.
1. is non-termination but repeating
2. terminates after two places of decimal
3. has a terminatiing decimal
4. is non-terminating and non-repeating

Answer 1

Correct Answer - Option 3 : has a terminatiing decimal

Concept:

A Number with the denominator form of 2^m 5ⁿ (m & n ∈ W (Whole Number)) has Terminal decimal Expansion.

Calculation:

Given Number, \(\dfrac{441}{2^2\times5^3\times7}\) = \(\dfrac{3^2\times 7^2}{2^2\times5^3\times7}\) = \(\dfrac{3^2\times 7}{2^2\times5^3}\) = \(\dfrac{63}{2^2\times5^3}\)

Where the denominator is in the form of 2^m 5ⁿ= 2² 5³with m = 2, n = 3.

Hence, the given number has a terminating decimal.