# The number

Question:

The number $\frac{665}{625}$ will terminate after how many decimal places?

Solution:

$\frac{665}{625}=\frac{5 \times 19 \times 7}{5^{4}}=\frac{19 \times 7}{5^{3}}=\frac{19 \times 7 \times 2^{3}}{5^{3} \times 2^{3}}=\frac{1064}{1000}=1.064$

So, $\frac{665}{625}$ will terminate after 3 decimal places.
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