The rational form of $4.0 ¯ ¯¯¯¯ ¯ 52$ is

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Solution

the method of expressing recurring decimal in $\frac{p}{q}$ from
is
recuring decimal $= \frac{w h o l e n u m b e r f o r m o f t h e n u m b e r - w h o l e n u m b e r o f n o n r e c u r i n g d i g i t}{10^{n o . o f d i g i t s a f t e r d e c i m a l} - 10^{n o . o f d i g i t s n o n r e c u r i n g a f t e r d e c i m a l}}$
Here,
$4.0 ¯ ¯¯¯¯ ¯ 52 = \frac{4052 - 40}{10^{3} - 10^{1}} = \frac{4012}{990}$

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