Convert 0.286 as a fraction.
Understand the Problem
The question is asking to convert the decimal 0.286 into a fraction format. This involves identifying the place value of the decimal and expressing it as a fraction.
Answer
$\frac{143}{500}$
Answer for screen readers
The decimal 0.286 as a fraction is $\frac{143}{500}$.
Steps to Solve
- Identify the Decimal Place Value
The decimal 0.286 has three digits after the decimal point. This means that it is in the thousandths place.
- Write the Fraction Form
To write the decimal as a fraction, place the decimal value over its place value. Since 0.286 is in the thousandths, we write it as: $$ \frac{286}{1000} $$
- Simplify the Fraction
Next, we need to simplify the fraction. We find the greatest common divisor (GCD) of 286 and 1000.
- Finding the GCD
The prime factorization of 286 is (2 \times 11 \times 13) and for 1000 it is (2^3 \times 5^3). The GCD is 2.
- Divide Both Numerator and Denominator by the GCD
Now we divide both 286 and 1000 by their GCD (which is 2): $$ \frac{286 \div 2}{1000 \div 2} = \frac{143}{500} $$
The decimal 0.286 as a fraction is $\frac{143}{500}$.
More Information
Converting decimals to fractions is a common mathematical operation that can help in understanding how decimal numbers relate to fractions. The process involves recognizing the place values and simplifying fractions when possible.
Tips
- Forgetting to simplify the fraction often leads to incorrect or non-optimized answers. Always check if you can reduce the fraction.
- Incorrectly identifying the place value of the decimal can lead to an inaccurate initial fraction.
