Convert the following repeating decimal to a fraction in simplest form.
point, 7, start overline, 6, end overline
To convert the repeating decimal 0.76̅ to a fraction, we'll use the following steps:
Let x = 0.76̅
Multiply x by 100 to move the decimal point two places to the right: 100x = 76.76̅
Subtract x from 100x to eliminate the repeating decimal: 100x - x = 76.76̅ - 0.76̅ = 76
Simplify the equation: 99x = 76
Divide both sides of the equation by 99: x = 76/99
Therefore, the repeating decimal 0.76̅ can be converted to the fraction 76/99 in its simplest form.