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=1/10B. a1=23, r=1/100C. a1=23/100, r=100D. a1=23/100, r=1/100
Accepted Solution
A:
Answer: D. a1=23/100, r=1/100Step-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.