Question

What is the fractional equivalent of 2.125 in simplest form?

*Your answer must be written as a mixed number.

Answer 1

To convert the decimal 2.125 into a mixed number, we can follow these steps:

1. **Separate the whole number from the decimal:**
The whole number part is 2.
The decimal part is 0.125.

2. **Convert the decimal part to a fraction:**
The decimal 0.125 can be written as \( \frac{125}{1000} \) since it has three decimal places (1 in the tenths place, 2 in the hundredths place, and 5 in the thousandths place).

3. **Simplify the fraction \( \frac{125}{1000} \):**
We need to find the greatest common divisor (GCD) of 125 and 1000.
The factors of 125 are \( 1, 5, 25, \) and \( 125 \).
The factors of 1000 are \( 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500, \) and \( 1000 \).
The GCD is 125.

Now we divide both the numerator and the denominator by their GCD:

\[
\frac{125 \div 125}{1000 \div 125} = \frac{1}{8}
\]

4. **Combine the whole number and the fraction:**
Now, we take the whole number 2 and add the simplified fraction \( \frac{1}{8} \):

\[
2 + \frac{1}{8} = 2 \frac{1}{8}
\]

Thus, the fractional equivalent of 2.125 in simplest form, written as a mixed number, is

\[
\boxed{2 \frac{1}{8}}
\]