Question

What fraction is equivalent to the decimal number 0.90¯¯¯¯¯
?(1 point)
Responses

1011
10 over 11

910
9 tenths

19
1 ninth

190

Answer 1

The decimal number \( 0.90\overline{0} \) (which represents \( 0.909090...\)) can be converted to a fraction.

Let's denote the repeating decimal as \( x \):

\[
x = 0.909090...
\]

To eliminate the repeating part, we can multiply both sides of the equation by \( 100 \) (since the repeating part is two digits):

\[
100x = 90.909090...
\]

Now we can subtract the first equation from this new equation:

\[
100x - x = 90.909090... - 0.909090...
\]

This simplifies to:

\[
99x = 90
\]

Now, we solve for \( x \):

\[
x = \frac{90}{99}
\]

We can simplify \( \frac{90}{99} \) by dividing both the numerator and denominator by their greatest common divisor, which is 9:

\[
x = \frac{10}{11}
\]

Thus, the fraction equivalent to the decimal number \( 0.90\overline{0} \) is:

**\(\frac{10}{11}\)**

So the correct response is:

**10 over 11**.