Question

Express 5.1 23 bar in p by Q form where p and q are co primes
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Answer 1

Answer:

$\frac{1703}{999}=5.123123123................$

Step-by-step explanation:

Let

x=5.123123123..............._______(1)

Multiply both sides by 1000

1000x=5123.123123123...........____(2)

subtract (1) from (2)

1000x-x=5123-5

999x=5118

$x=\frac{5118}{999}$

$\implies\,x=\frac{1706}{333}$

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Answer 2

$5.\overline{123}=\frac{1706}{3\times 111}$

Step-by-step explanation:

To find : Express 5.1 23 bar in p by q form where p and q are co primes?

Solution :

Let $x=5.123123......$ ....(1)

Multiply both side by 1000,

$1000x=5123.123123...$ .....(2)

Subtract (1) and (2),

$1000x-x=(5123.123123....)-(5.123123.....)$

$999x=5118$

$x=\frac{5118}{999}$

$x=\frac{1706}{333}$

$x=\frac{1706}{3\times 111}$

As p=1706 and $q=3\times 111$ are co-primes.

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