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Express 4.142‾4.\overline{142}4.142​ in the form pq\frac{p}{q}qp​​, where p and q are integers and q≠0.
Question

Express 4.1424.\overline{142}​ in the form pq\frac{p}{q}​, where p and q are integers and q0.

A.

4142999\frac{4142}{999}​​

B.

4136999\frac{4136}{999}​​

C.

4140999\frac{4140}{999}​​

D.

4138999\frac{4138}{999}​​

Correct option is D

Given:

Given number =4.1424.\overline{142}​​

Solution:

Let x = 4.142142…

Then 1000x = 4142.142…

1000x - x = 4142.142142… - 4.142142..

999x = 4138

x =4138999 \frac{4138}{999}​​

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