Write the repeating decimal as a ratio of integers.
-0.363636

Question

Quizplus · Accepted Answer

To convert the repeating decimal into a fraction, we can assign a variable (let's say x) to the repeating part (0.36), and then subtract the non-repeating part (0.36) to get:

x = 0.363636...
100x = 36.3636...

Subtracting the first equation from the second eliminates the repeating part:

99x = 36
x = 36/99

The fraction can be simplified by dividing both the numerator and denominator by the greatest common factor (which is 3 in this case):

x = 12/33 = 4/11

Therefore, the repeating decimal 0.363636... is equal to the fraction 4/11.

Out of the given choices, only option C has the fraction 4/11.

Write the Repeating Decimal as a Ratio of Integers