0.045 (overlined)
what is the fraction for the decimal expansion above?
A. 1/25
B. 4/45
C. 4/9
D. 1/22
The fraction for the decimal expansion 0.045 (overlined) is 4/9.
The overline above the 5 indicates that it repeats infinitely. To convert it to a fraction, we can set x = 0.045 (overlined) and subtract it from x = 45.045 (overlined) to eliminate the repeating decimal:
x = 0.045 (overlined)
1000x = 45.045 (overlined)
Subtracting the first equation from the second equation, we have:
1000x - x = 45.045 - 0.045
999x = 45
Dividing both sides by 999, we get:
x = 45/999
Simplifying this fraction by dividing both the numerator and denominator by 9, we have:
x = 5/111
However, this fraction is not one of the answer choices given.
Therefore, there may be an error in the options for this question, as none of them correctly represent the fraction for the given decimal.
thats not true
Apologies for the confusion. Let's solve the problem again.
To convert the decimal 0.045 (overlined), let's denote it as x:
x = 0.045 (overlined)
Multiplying both sides by 1000 to eliminate the decimal:
1000x = 45.045 (overlined)
Now, subtracting the original equation from the new equation:
1000x - x = 45.045 (overlined) - 0.045 (overlined)
This simplifies to:
999x = 45
Dividing both sides by 999:
x = 45/999
Simplifying the fraction by dividing both the numerator and denominator by 9:
x = 5/111
Therefore, the fraction for the decimal 0.045 (overlined) is 5/111.
The correct answer is not listed among the options provided.