Multiply the following repeating decimals by 10, 100 and 1000.

This is a terminating decimal.
$0.53 = \frac{53}{100}$
Terminating decimals are rational.
Rational

This is a terminating decimal.
$0.218 = \frac{218}{1000} = \frac{109}{500}$
Rational

This is a terminating decimal.
$0.396 = \frac{396}{1000} = \frac{99}{250}$
Rational

This is a repeating decimal.
Let $x = 0.\overline{52}$.

Repeating decimals are rational.
Rational

: Convert repeating decimals to fractions

Let $x = 0.\overline{16}$.

\dfrac{16}{99}

Let $x = 0.\overline{6}$.

$x = \frac{6}{9} = \frac{2}{3}$.
\dfrac{2}{3}

Let $x = 0.\overline{25}$.

$x = \frac{25}{99}$.
\dfrac{25}{99}

Let $x = 0.\overline{46}$.

$x = \frac{46}{99}$.
\dfrac{46}{99}