Question

Use the infinite geometric sum formula to write 0.757575... as a fraction in reduced form.

Answer 1

In the given above, we have the decimal number, 0.75757575.. where digits 7 and 5 are repeated. The reduced form for decimal numbers with repeated digits is to divide the number by 9 (number of 9 depends on the repeating digits). This is as follows,

                       f = 75/99

We may divide the numbers ins the denominator and numerator by 3 to come up with the reduced form which is equal to 25/33.

Answer: 25/33