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20 September, 11:53

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?

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  1. 20 September, 12:08
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    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
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