Question

Which of these statements is true about the decimal form of the number shown?
25/225


A.
It is neither a terminating decimal nor a repeating decimal.
B.
It is a terminating decimal.
C.
It is both a terminating decimal and a repeating decimal.
D.
It is a repeating decimal.

Answer 1

First, let's simplify the fraction \( \frac{25}{225} \).

Both the numerator and the denominator can be divided by 25:

\[
\frac{25 \div 25}{225 \div 25} = \frac{1}{9}
\]

Next, we need to analyze the decimal form of \( \frac{1}{9} \).

When we convert \( \frac{1}{9} \) to a decimal, it results in:

\[
1 \div 9 = 0.1111\ldots
\]

This decimal can also be represented as \( 0.\overline{1} \), which indicates that the digit "1" repeats indefinitely.

Now, let's evaluate the options:

- **A. It is neither a terminating decimal nor a repeating decimal.** (False)

- **B. It is a terminating decimal.** (False)

- **C. It is both a terminating decimal and a repeating decimal.** (False)

- **D. It is a repeating decimal.** (True)

Therefore, the correct answer is:

**D. It is a repeating decimal.**