Question

Without actual division show that 43/160 ise xpressible as a terminating decimal . Give reason .

Answer 1

Answer:

0.26875

Step-by-step explanation:

$\frac{43}{160}=\frac{43}{2\times 2\times 2\times 2\times 2\times 5}=\frac{43}{2^5\times 5}$

Here denominator is of the form $2^n\times 5^m$, hence 43/160 has terminating decimal expansion.

To convert in decimal we need to multiply numerator and denominator by $5^{4}$.

$\frac{43\times 5^4}{2^5\times 5\times 5^4}=\frac{43\times 625}{2^5\times 5^5}=\frac{26875}{(2\times5)^5}=\frac{26875}{10^5}=0.26875$

Note: If a reduced fraction's denominator has only 2 and 5 or either of them as its factors then decimal expansion is always terminating.