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Byju's Answer
Standard IX
Mathematics
Expressing Decimals as Rational Numbers
Express the f...
Question
Express the following in the form
p
q
, where
p
and
q
are integers and
q
≠
0
0.404040...
=
40
q
, then what is the value of
q
?
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Solution
Let
x
=
0.404040...
=
>
100
x
=
40.4040...
=
>
100
x
=
40
+
0.4040...
=
>
100
x
=
40
+
x
=
>
100
x
−
x
=
40
=
>
99
x
=
40
=
>
x
=
40
99
Hence,
q
=
99
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