Question

0.790 repeating as a fraction

Answer 1

To convert a repeating decimal into a fraction, we can use a property of infinite geometric series.

Let x = 0.790 repeating
Multiplying both sides by 1000 to move the decimal point:
1000x = 790.790 repeating
Subtracting the first equation from the second equation:
1000x - x = 790.790 repeating - 0.790 repeating
999x = 790
Dividing both sides by 999 to solve for x:
x = 790 / 999

So, 0.790 repeating can be written as the fraction 790/999.