The formula for the sum of an infinite geometric series, s=a1/1-4 may be used to convert 0.23 to a fraction. what are the values?

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