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Express 5.7ˉ5.\bar{7}5.7ˉ in pq\frac{p}{q}qp​ form, where p and q are integers and q≠0q \ne 0q=0​​
Question

Express 5.7ˉ5.\bar{7} in pq\frac{p}{q} form, where p and q are integers and q0q \ne 0​​

A.

527\frac{52}{7}​​

B.

529\frac{52}{9}​​

C.

5710\frac{57}{10}​​

D.

577\frac{57}{7}​​

Correct option is B

Given:

Given 5.7ˉ5.\bar{7}​​

Solution:

Let x = 5.777…

Then 10x = 57.77..

10x-x = 57.77…-5.777..

9x = 52

x = 529\frac{52}{9}​​

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