How you would convert the repeating, nonterminating decimal to a fraction? Explain the process as you solve the problem. 0.1515 . . .

Answer 1

To convert the repeating, nonterminating decimal 0.1515... to a fraction, we can first observe that the decimal part "15" repeats indefinitely. To represent a repeating decimal as a fraction, we can use the concept of geometric series.

Let x = 0.1515...

Multiplying x by 100 to shift the decimal two places:

100x = 15.1515...

Now, subtract the initial equation from the second equation to eliminate the repeating part:

100x - x = 15.1515... - 0.1515...
99x = 15

Now, we can solve for x by dividing both sides of the equation by 99:

99x/99 = 15/99
x = 15/99

Simplifying the fraction by dividing the numerator and denominator by their greatest common divisor (which is 3):

x = 5/33

Therefore, the repeating decimal 0.1515... is equivalent to the fraction 5/33.