Question

A real number $\frac{2^2\times 3^2\times 7^2}{2^5\times 5^3\times 3^2\times 7}$ will have _________.

• A. Terminating decimal
• B. Non-terminating decimal
• C. Non-terminating and non-repeating decimal
• D. Terminating repeating decimal

Answer 1

Answer: (A)

Terminating decimal

Using the law of exponent,

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

$=2^{-3}\times 3^0\times 5^{-3}\times 7^1$

$=\frac{7}{2^3\times 5^3}$

$=\frac{7}{1000}$ $=0.007$.

$\therefore 0.007$ is a terminating and non-repeating decimal.

That is, option $A$ is correct.