Question

Which simplified fraction represents 0.ModifyingAbove 45 with bar?
StartFraction 45 Over 99 EndFraction
StartFraction 99 Over 45 EndFraction
StartFraction 5 Over 11 EndFraction
StartFraction 11 Over 5 EndFraction

Answer 1

To express the repeating decimal \( 0.\overline{45} \) as a fraction, we can use the following method:

Let \( x = 0.\overline{45} \).

Then, multiplying both sides by 100 (since the repeat is over 2 digits):

\[
100x = 45.\overline{45}
\]

Now we subtract the original equation \( x = 0.\overline{45} \) from this equation:

\[
100x - x = 45.\overline{45} - 0.\overline{45}
\]

This simplifies to:

\[
99x = 45
\]

Now, we divide both sides by 99:

\[
x = \frac{45}{99}
\]

Next, we simplify the fraction \( \frac{45}{99} \). Both the numerator and denominator can be divided by their greatest common divisor (GCD), which is 9:

\[
\frac{45 \div 9}{99 \div 9} = \frac{5}{11}
\]

Thus, the simplified fraction that represents \( 0.\overline{45} \) is

\[
\frac{5}{11}.
\]

Therefore, the correct answer is

\[
\text{StartFraction 5 Over 11 EndFraction}.
\]