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Question
What is 0.825
written as a fraction? Express your answer as a fraction in simplified form.(1 point)

Answer 1

To convert the decimal \(0.825\) to a fraction, we can follow these steps:

1. Write \(0.825\) as a fraction, placing it 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):
\[
\frac{0.825 \times 1000}{1 \times 1000} = \frac{825}{1000}
\]

3. Now we need to simplify the fraction \(\frac{825}{1000}\). We 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 factors are \(5\). The GCD is \(5\).

4. Now, divide both the numerator and the denominator by the GCD:
\[
\frac{825 \div 5}{1000 \div 5} = \frac{165}{200}
\]

5. We can simplify further:
- The GCD of \(165\) and \(200\) is \(5\).
- So, we divide again:
\[
\frac{165 \div 5}{200 \div 5} = \frac{33}{40}
\]

Thus, \(0.825\) as a simplified fraction is:
\[
\frac{33}{40}
\]