Question

p/q form of 83.543543​

Answer 1

Answer:

83460/999

Step-by-step explanation:

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Answer 2

Question :-

Express 83.543543... in the Form $\frac{p}{q}$, where p and q are Integers and q ≠ 0.

Solution :-

Let x = 83.543543543...     ...(i)

Since the Repeating Block 543 has Three Digits, we Multiply x by 1,000 to get

1000x = 83543.543543...     ...(ii)

Subtracting (i) from (ii), we get -

999x = 83,460.000000 $\Leftrightarrow$ 999x = 83,460

∴ x = $\frac {83,460}{999}$ = $\bold {\frac{27,820}{333}}$

Hence, $\bold {83.\overline {543} = \frac{27,820}{333}}$ .

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