Question

Convert 0.45¯¯¯¯¯ to a fraction.(1 point) The fraction that is equivalent to 0.45¯¯¯¯¯ is

Answer 1

To convert the repeating decimal \( 0.45\overline{45} \) to a fraction, we can use the following steps:

Let \( x = 0.454545\dots \).

Since the repeating part has two digits (45), we can multiply \( x \) by 100 to shift the decimal point two places to the right:

\[
100x = 45.454545\dots
\]

Next, we can set up an equation using the original \( x \):

\[
x = 0.454545\dots
\]

Subtract the first equation from the second equation:

\[
100x - x = 45.454545\dots - 0.454545\dots
\]
\[
99x = 45
\]

Now, divide both sides by 99:

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

Next, simplify the fraction. Both 45 and 99 can be divided by their greatest common divisor, which is 9:

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

Thus, the fraction that is equivalent to \( 0.45\overline{45} \) is

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