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Express 123.47‾123.4\overline{7}123.47 in  pq\frac{p}{q}qp​​  form, where p and q are integers and q≠0q≠ 0q=0​.
Question

Express 123.47123.4\overline{7} in  pq\frac{p}{q}​  form, where p and q are integers and q0q≠ 0​.

A.

1234799\frac{12347}{99}​​

B.

1111390\frac{11113}{90}​​

C.

1234790\frac{12347}{90}​​

D.

111139\frac{11113}{9}​​

Correct option is B

Given:

123.47123.4\overline{7}​​

Solution:

Let x = 123.4777…

Then 10x = 1234.777…

And 100x = 12347.77…

100x -10x = 12347.777… - 1234.777…

90x = 11113

x = 1111390 \frac{11113}{90}​​

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