Express the following decimals as rational numbers in the form of $\frac{p}{q}$ :
$- 0.125$

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Solution

$0.125 = 1$ tenths $+ 2$ hundredths $+ 5$ thousandths $\Rightarrow 0.125 = 1 \times \frac{1}{10} + 2 \times \frac{1}{100} + 5 \times \frac{1}{1000}$
$0.125 = \frac{1}{10} + \frac{2}{100} + \frac{5}{1000} = \frac{100}{1000} + \frac{20}{1000} + \frac{5}{1000} = \frac{100 + 20 + 5}{1000} = \frac{125}{1000}$
$\frac{125}{1000}$ gets reduced $\frac{1}{8}$
Hence, final form is $\frac{- 1}{8}$

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Similar questions

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