Question

Write down the decimal expansions of the following rational numbers by writing their denominators in the form 2^m × 5ⁿ, where, m, n are non-negative integers.$$\frac{14588}{625}$$

Answer 1

The given number is $$\frac{14588}{625}$$ Clearly, 625 = 5⁴ is of the form 2^m × 5ⁿ, where m = 0 and n = 4.

So, the given number has terminating decimal expansion.

$$\therefore \frac{14588}{625}=\frac{14588\times 2^4}{2^4\times 5^4}=\frac{14588\times 16}{{(2\times 5)}^4}=\frac{233408}{{\left(10\right)}^4}=\frac{233408}{10000}=23.3408$$