0.045 (overlined)
what is the fraction for the decimal expansion above?
A. 1/25
B. 4/45
C. 4/9
D. 1/22
To find the fraction for the decimal expansion 0.045 (overlined), let us call the decimal expansion x. Then, we can write the equation:
x = 0.045 (overlined)
To get rid of the decimal and the overline, we can multiply both sides of the equation by 1000 (since the overline represents repeating, we multiply by 1000 to shift the decimal point three places to the right):
1000x = 45.045 (overlined)
Since there is a repeating pattern after the decimal point, we can subtract the original equation from the new equation to eliminate the repeating part:
1000x - x = 45.045 (overlined) - 0.045 (overlined)
999x = 45
Dividing both sides of the equation by 999:
x = 45/999.
Simplifying the fraction, we can divide both the numerator and denominator by 9 to get:
x = 5/111.
Therefore, the fraction for the decimal expansion 0.045 (overlined) is 5/111.