Question

Express the decimal as a fraction. Be sure the fraction is in simplest form.
0.825

Answer 1

To express the decimal \(0.825\) as a fraction, follow these steps:

1. Write the decimal as a fraction over 1:
\[
0.825 = \frac{0.825}{1}
\]

2. To eliminate the decimal, multiply both the numerator and the denominator by 1000 (since there are three digits after the decimal point):
\[
\frac{0.825 \times 1000}{1 \times 1000} = \frac{825}{1000}
\]

3. Next, simplify the fraction \(\frac{825}{1000}\). To do this, find the greatest common divisor (GCD) of 825 and 1000.

The prime factorization of 825 is:
\[
825 = 3 \times 5^2 \times 11
\]
The prime factorization of 1000 is:
\[
1000 = 10^3 = 2^3 \times 5^3
\]
The common factor is \(5^2\), which is 25.

4. Divide both the numerator and the denominator by their GCD, 25:
\[
\frac{825 \div 25}{1000 \div 25} = \frac{33}{40}
\]

Therefore, the decimal \(0.825\) as a fraction in simplest form is:
\[
\frac{33}{40}
\]