Convert 0.27 (repeating decimal) to a rational number in simplest form. (1 point)

Question

A. 27/100
B. 3/11
C. 1/27
D. 27/99

Answer 1

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. \( \frac{3}{11} \).

Answer 2

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