Question

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

Answer 1

Let \( x = 0.454545...\), where the "45" repeats indefinitely.

To eliminate the repeating decimal, we can multiply \( x \) by 100, since there are two digits in the repeating part:

\[
100x = 45.454545...
\]

Now we can set up the equations:

1. \( x = 0.454545...\)
2. \( 100x = 45.454545...\)

Next, we subtract the first equation from the second:

\[
100x - x = 45.454545... - 0.454545...
\]

This simplifies to:

\[
99x = 45
\]

Now, we solve for \( x \):

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

Now, we simplify the fraction. Both the numerator and the denominator can be divided by 9:

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

Thus, the fraction that is equivalent to \( 0.45¯¯¯¯¯ \) is

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