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When 0.434343..... is converted into a fraction, then the result will be :
Question

When 0.434343..... is converted into a fraction, then the result will be :

A.

43100\frac{43}{100}​​

B.

4.30.1\frac{4.3}{0.1}​​

C.

439.9\frac{43}{9.9}​​

D.

4399\frac{43}{99}​​

Correct option is D

Given:

Repeating decimal = 0.434343...

Solution:
Let x = 0.430.\overline{43}​​
Then multiplying both sides by 100 (since 2 digits repeat):

100x = 43.4343.\overline{43}​​

Now subtracting:

100xx=43.430.43 99x=43 x=4399100x - x = 43.\overline{43} - 0.\overline{43} \\ \ \\ 99x = 43 \\ \ \\ x = \frac{43}{99}​​

0.434343...=43990.434343... = \frac{43}{99}​​

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