Question

what is 0.825 written as a fraction express your answer as a fraction in simplified form

Answer 1

To convert the decimal 0.825 to a fraction, follow these steps:

1. Write 0.825 as a fraction:
\[
0.825 = \frac{825}{1000}
\]

2. Simplify the fraction by finding the greatest common divisor (GCD) of 825 and 1000.

First, let's factor both numbers:
- \(825 = 3 \times 5^2 \times 11\)
- \(1000 = 10^3 = 2^3 \times 5^3\)

The common factors are \(5^2\). Therefore, the GCD is \(25\).

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

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