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Verified Answer :

You've been given the answer - but I'll provide one method:

Let x = 8.132132132....

1000x = 8132.132132132.... (It's a repeating decimal)

999x = 8124 (1000x - x, repeating decimals cancel)

x = 8124/999 (Divide by 999)

I hope my answer has come to your help. God bless and have a nice day ahead!

Answer:

\(\text{The rational form is }\frac{8124}{999}\)    

Step-by-step explanation:

Given the number 8.132132....

we have to convert the above number to a rational expression.

\(\text{Let x=}8.132132.....\)  → (1)

Multiply by 1000 on both sides

\(1000x=8132.132132...\)    →  (2)

Subtracting equation (1) from equation (2), we get

\(999x=8124\)

Divide throughout by 999, we get

\(x=\frac{8124}{999}\)

which is required rational form.

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