UB001 wrote:

If the digits 53 in the decimal 0.00053 repeat indefinitely, what is the value of (10^5-10^3)(0.00053)?

A. 0

B. 0.53 repeating

C. 5.3

D. 10

E. 53

We know how to deal with recurring decimals. Say,

\(.000535353... = x\)

\(.535353... = 1000x\) ... (I)

\(53.535353... = 100000x\) ... (II)

(II) - (I)

\((100000 - 1000)x = 53\)

\(x = \frac{53}{(10^5 - 10^3)}\)

So we get that \(0.000535353... = \frac{53}{(10^5 - 10^3)}\)

Let's put it in our original expression:

\((10^5-10^3)(0.00053) = (10^5-10^3)*\frac{53}{(10^5 - 10^3)} = 53\)

Answer (E)

Here is a post on our

Veritas Prep blog that gives details of this method:

https://www.veritasprep.com/blog/2014/0 ... fractions/
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Karishma

Veritas Prep GMAT Instructor

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