Question

Convert 0.27¯¯¯¯¯ to a rational number in simplest form.(1 point)
Responses

27/100
Start Fraction 27 over 100 end fraction

3/11
Start Fraction 3 over 11 end fraction

1/27
Start Fraction 1 over 27 end fraction

27/99

Answer 1

Let \( x = 0.27\overline{27} \).

To convert this repeating decimal to a fraction, first express it as:

\[
x = 0.272727\ldots
\]

Next, to eliminate the repeating part, we can multiply \( x \) by 100 (since the repeating part has 2 digits):

\[
100x = 27.272727\ldots
\]

Next, subtract the original \( x \) from this equation:

\[
100x - x = 27.272727\ldots - 0.272727\ldots
\]

This simplifies to:

\[
99x = 27
\]

Now, solve for \( x \):

\[
x = \frac{27}{99}
\]

To simplify \( \frac{27}{99} \):

Both the numerator and denominator can be divided by 9:

\[
\frac{27 \div 9}{99 \div 9} = \frac{3}{11}
\]

Thus, the rational number in simplest form is:

\[
\frac{3}{11}
\]

So, the answer is:

**3/11** (Start Fraction 3 over 11 end fraction).