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Convert 0.236‾0.2\overline{36}0.236​  into a regular fraction.
Question

Convert 0.2360.2\overline{36}​  into a regular fraction.

A.

733\frac{7}{33}​​

B.

944\frac{9}{44}​​

C.

1766\frac{17}{66}​​

D.

1355\frac{13}{55}​​

Correct option is D

​​Given:
Recurring decimal 0.23636...

Solution:

Let X = Multiply X by 10

10X = 2.36......  (1)

1000X = 236.36.... (2)

Subtract (2) from  (1)

1000X - 10X = 236.36... - 2.36...

990X = 234

X = 234990\frac {234}{990}​​

X = 1355\frac {13}{55}​​

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