To convert the decimal 0.825 to a fraction, you can follow these steps:
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Write the decimal as a fraction with 1 in the denominator: \[ 0.825 = \frac{0.825}{1} \]
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To eliminate the decimal, multiply the numerator and the denominator by 1000 (since there are three digits after the decimal): \[ \frac{0.825 \times 1000}{1 \times 1000} = \frac{825}{1000} \]
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Now, simplify the fraction \(\frac{825}{1000}\):
- Find the greatest common divisor (GCD) of 825 and 1000. The GCD is 25.
- Divide both the numerator and the denominator by the GCD: \[ \frac{825 \div 25}{1000 \div 25} = \frac{33}{40} \]
Therefore, 0.825 written as a fraction is \(\frac{33}{40}\).