0.045 (overlined)
what is the fraction for the decimal expansion above?
To find the fraction for the decimal expansion, we can look at the digits after the decimal point.
Since the digit 0 is repeated after the decimal point, we can write it as 0.045 = 0.045045045...
To determine the fraction equivalent, let's call it x, we can multiply x by 1000 to move the decimal point three places to the right: 1000x = 45.045045045...
Now, we can subtract x from 1000x to eliminate the repeating decimals:
1000x - x = 45.045045045... - 0.045045045...
Simplifying the right side:
999x = 45
Dividing both sides by 999:
x = 45/999
Therefore, the fraction for the decimal expansion 0.045 (overlined) is 45/999.