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

The value of is 0.23 and the value of r is 1/100 and this can be determined by using the concept of geometric progression.

Given :

The formula for the sum of an infinite geometric series, .Fraction -- 0.23 (Repeated)

The following steps can be used in order to determine the values of and r:

Step 1 - The given repeated fraction can be written as:

                     0.2323232323... = 0.23 + 0.0023 + 0.000023 +...

Step 2 - The above series is in geometric progression.Step 3 - So, the value of is 0.23.Step 4 - The value of the geometric ratio can be calculated as:

                 

                 

The value of is 0.23 and the value of r is 1/100.

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I believe the number to be converted to a fraction is 0.232323..., this is 0.23 periodic.

The fomula is right:

 

Where   is 0.23 and r is 1/100

Check it here:

    23/100          23/100         23
-------------- =    ----------- =   ------- = 0.232323...
1 - 1/100          99/100          99

So, the answer is     23/100 and r = 1/100

D

Explanation: