Question

The formula for the sum of an infinite geometric series, S=a1/1-r, may be used to convert

0.23 (repeated) to a fraction. What are the values of a1 and r?

A. a1=23/10, r=1/10
B. a1=23, r=1/100
C. a1=23/100, r=100
D. a1=23/100, r=1/100

Answer 1

Explanation:

Here, a1 = 0.23 and r = 0.01. Thus, the sum of this infinite series will be

a1 0.23 0.23

------- = ------------- = ----------- = 23/99.

1 - r 1 - 1/100 99/100

Check this by dividing 23 by 99 on a calculator. Result: 0.23232323....

Answer 2

D. a1=23/100, r=1/100

Explanation:

The repeating fraction can be written as the sum ...

`0.\overline{23}=0.23+0.0023+0.000023+\dots`

The first term is a1 = 0.23 = 23/100, and each successive term is shifted 2 decimal places to the right, so is multiplied by the common ratio r=1/100.