nathanboff
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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

Respuesta :

sqdancefan

Answer:

  D.  a1=23/100, r=1/100

Step-by-step explanation:

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

[tex]0.\overline{23}=0.23+0.0023+0.000023+\dots[/tex]

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.

altavistard

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....

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