Question

Convert the following repeating decimal to a fraction simplest form
.32 ̅

Answer 1

To convert a repeating decimal to a fraction, we need to identify a pattern and create an equation to solve for the fraction value.

Let's denote the repeating decimal as x:
x = .32̅

To eliminate the repeated part, we can multiply x by 100 to shift the repeating part two digits to the left:
100x = 32.32̅

Now, subtract the original value of x from 100x:
100x - x = 32.32̅ - .32̅
99x = 32

To isolate x, divide both sides of the equation by 99:
x = 32/99

Therefore, the fraction equivalent of the repeating decimal .32̅ is 32/99.