Question

The decimal expansion of the rational number 21567/6250 will terminate after how many places in decimal????​

Answer 1

$Given \: Rational \: number \: \frac{21567}{6250}$

$= \frac{21567}{625 \times 10}$

$= \frac{21567}{5^{4} \times 5\times 2}$

$= \frac{21567}{5^{5} \times 2}$

$= \frac{21567\times 2^{4}}{5^{5} \times 2\times 2^{4}}$

$= \frac{21567\times 16}{5^{5} \times 2^{5}}$

$= \frac{345072}{(5\times 2)^{5}}$

$= \frac{345072}{(10)^{5}}$

$= 3.45072$

Therefore.,

$\red{Decimal \: expansion \: of \: \frac{21567}{6250}}$

$\green { = 3.45072}$

After 5 decimal places it terminates.

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