Convert the following repeating decimal to a fraction in simplest form.
., start overline, 8, 3, end overline
.
83
The repeating decimal .83̅ can be expressed as a fraction by following these steps:
Let x be the repeating decimal.
Multiply both sides of the equation x = .83̅ by 100 to move the decimal point two places to the right:
100x = 83.̅
Subtract the original equation from the multiplied equation to eliminate the repeating part:
100x - x = 83.̅ - .83̅
99x = 83
Divide both sides of the equation by 99 to solve for x:
99x/99 = 83/99
x = 83/99
Therefore, the repeating decimal .83̅ can be simplified as the fraction 83/99.