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Chapter 1: Q3P (page 1)

Use equation (1.8) to find the fractions that are equivalent to the following repeating decimals:

0.55555...

Short Answer

Expert verified

The equivalent fraction for0.55555... is 59.

Step by step solution

01

Explanation of solution

Given number is 0.55555....

The expression for sum of infinite GP series is S=a1-r.

Where, S is the sum of GP up to infinite terms.

02

Equivalent fraction

Fractions having the same numerator and denominator but different numerators and denominators are called equivalent fractions.

03

Calculation

An example of how to write the number is as follows:

0.55555...=0.5+0.05+0.005+0.0005+....+0.5110n

The words will create GP with a=0.5and r=1/10.

Substitute 0.5 for a and 1/10 for r in above equation.

S=0.51-110=510910=59

Hence, the fraction is 59.

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