Convert 0.85 to a fraction.
Understand the Problem
The question is asking how to convert the decimal number 0.85 into a fraction. This involves expressing the decimal as a ratio of two integers.
Answer
The fraction representation is $\frac{17}{20}$.
Answer for screen readers
The fraction representation of the decimal 0.85 is $\frac{17}{20}$.
Steps to Solve
- Write the Decimal Over 1
Start by writing the decimal number as a fraction over 1.
$$ \frac{0.85}{1} $$
- Eliminate the Decimal
To remove the decimal, multiply the numerator and the denominator by 100 (since there are two digits after the decimal point).
$$ \frac{0.85 \times 100}{1 \times 100} = \frac{85}{100} $$
- Simplify the Fraction
Now simplify the fraction by finding the greatest common divisor (GCD) of the numerator and the denominator. The GCD of 85 and 100 is 5.
Divide both the numerator and the denominator by their GCD:
$$ \frac{85 \div 5}{100 \div 5} = \frac{17}{20} $$
The fraction representation of the decimal 0.85 is $\frac{17}{20}$.
More Information
Converting decimals to fractions is a useful skill in mathematics. Knowing that $0.85$ represents 85 out of 100 helps demonstrate how decimals and fractions relate to each other.
Tips
- Forgetting to multiply both the numerator and the denominator by the same number (e.g., 100).
- Failing to simplify the fraction at the end. Always check for the GCD.
