   Chapter 13.3, Problem 78E ### Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742

#### Solutions

Chapter
Section ### Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742
Textbook Problem

# SKILLS77-82 ■ Repeated Decimal Express the repeating decimal as a fraction. 0.2 53 ¯

To determine

The repeating decimal of 0.253¯ as a fraction.

Explanation

Approach:

If |r|<1, then the infinite geometric series converges.

k=1ark1=a+ar+ar2+ar3+

The sum of the infinite geometric series, when it is convergent is given as,

S=a1r ……(1)

Here, S is the sum of infinite geometric series, a is the first term of the sequence and r is the common ratio of the sequence.

If |r|1, then the infinite geometric series diverges.

Calculation:

The repeating decimal can be written as a series,

210+531000+53100,000+

Since the first term of the sequence is 531000 and the common ratio is 1100

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