Question

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

Answer 1

Answer:

  D.  a1=23/100, r=1/100

Step-by-step 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.

Answer 2

Answer:

Step-by-step 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....