Question

Convert 0.27 (repeating decimal) to a rational number in simplest form. (1 point)
A. 27/100
B. 3/11
C. 1/27
D. 27/99

Answer 1

To convert 0.264 (epeating decimal) to a rational number, you would set x equal to 0.264 and then multiply both sides of the equation by what number? (1 point)
100
10
1,000
999

Answer 2

To convert the repeating decimal \(0.27\) (where \(27\) repeats) into a rational number, let us denote it as \(x\):

\[
x = 0.27272727\ldots
\]

Next, we can multiply both sides by \(100\) to shift the decimal point two places to the right:

\[
100x = 27.27272727\ldots
\]

Now, we can set up a second equation with just \(x\):

\[
x = 0.27272727\ldots
\]

Now, we'll subtract the first equation from the second:

\[
100x - x = 27.27272727\ldots - 0.27272727\ldots
\]

This simplifies to:

\[
99x = 27
\]

Now, we solve for \(x\):

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

Next, we simplify \(\frac{27}{99}\). The greatest common divisor (GCD) of \(27\) and \(99\) is \(9\):

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

Thus, \(0.27\) (repeating) as a rational number in simplest form is:

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

Therefore, the correct answer is **B. \( \frac{3}{11} \)**.