Answer:
a₁ = 23/100 and r = 1/100
S = 23/99
Step-by-step explanation:
The sum of an infinite geometric series is:
S = a₁ / (1 − r)
where a₁ is the first term of the series and r is the common ratio.
0.23 repeating is 0.232323... To convert this to a fraction using the above equation, first we must write this as a series:
0.23 repeating = 0.23 + 0.0023 + 0.000023 + ...
The first term is 0.23, and the common ratio is 0.01.
Therefore, a₁ = 0.23 and r = 0.01. Or, in fraction form, a₁ = 23/100 and r = 1/100.
Plugging this into the equation, we can convert 0.232323... to a fraction.
S = (23/100) / (1 − 1/100)
S = (23/100) / (99/100)
S = 23/99
