Final answer:
To find the fraction that represents the repeating decimal of 0.77, we need to identify the repeating part. By setting up an equation and solving it, we find that the fraction is 76.23/99.
Step-by-step explanation:
To find the fraction that represents the repeating decimal of 0.77, we first need to identify the repeating part of the decimal. In this case, the repeating part is 77. To express this as a fraction, we set up an equation where x represents the repeating part:
x = 0.77
Multiplying both sides of the equation by 100 (to shift the decimal point two places to the right) gives us:
100x = 77
Subtracting the two equations:
100x - x = 77 - 0.77
99x = 76.23
Dividing both sides of the equation by 99:
x = 76.23/99
Simplifying the fraction on the right side of the equation:
x = 0.77
Therefore, the fraction that represents the repeating decimal of 0.77 is 76.23/99.