0.845 as a fraction
Understand the Problem
The question is asking how to convert the decimal number 0.845 into a fraction. This involves identifying the place value of the decimal and simplifying the resulting fraction.
Answer
The fraction equivalent of 0.845 is $\frac{169}{200}$.
Answer for screen readers
The fraction equivalent of 0.845 is $\frac{169}{200}$.
Steps to Solve
- Identify the place value of the decimal
The decimal number 0.845 has three digits after the decimal point. This means it can be expressed as a fraction over 1000 (since $10^3 = 1000$). So, we write:
$$ 0.845 = \frac{845}{1000} $$
- Simplify the fraction
Next, we need to simplify the fraction $\frac{845}{1000}$. We do this by finding the greatest common divisor (GCD) of 845 and 1000.
The GCD of 845 and 1000 is 5. Now we divide both the numerator and the denominator by their GCD:
$$ \frac{845 \div 5}{1000 \div 5} = \frac{169}{200} $$
- Final Fraction
Thus, the simplified fraction for the decimal 0.845 is:
$$ \frac{169}{200} $$
The fraction equivalent of 0.845 is $\frac{169}{200}$.
More Information
Converting decimals to fractions can often simplify mathematical problems, especially in algebra. The process involves identifying the place value and simplifying the fraction when necessary.
Tips
- Forgetting to simplify: A common mistake is stopping at the fraction $\frac{845}{1000}$ and not simplifying it further.
- Incorrectly identifying the GCD: Miscalculating the GCD can lead to incorrect simplifications, so it's essential to check the factors of the numbers properly.
