To write a fraction as a decimal, divide the numerator by the denominator. Plus, for example, the fraction ( \frac{3}{4} ) becomes the decimal 0. 75 because (3 \div 4 = 0.75). Understanding this process helps you convert fractions in calculations, compare quantities, solve problems, and recognize relationships between fractions and decimals It's one of those things that adds up..
Not obvious, but once you see it — you'll see it everywhere Worth keeping that in mind..
The Basic Principle: Division
Every fraction represents a division. The fraction ( \frac{a}{b} ) means that (a) is divided by (b). So, converting a fraction to a decimal is simply a matter of performing that division.
For example:
[ \frac{5}{10} = 5 \div 10 = 0.5 ]
[ \frac{7}{10} = 7 \div 10 = 0.7 ]
[ \frac{9}{10} = 9 \div 10 = 0.9 ]
Fractions with a denominator of 10 are especially easy to convert because each decimal place represents a different power of ten:
- ( \frac{1}{10} = 0.1 )
- ( \frac{1}{100} = 0.01 )
- ( \frac{1}{1,000} = 0.001 )
You can use this pattern when converting other fractions by first rewriting them with a denominator of 10, 100, 1,000, or another power of ten.
Step-by-Step Method for Converting a Fraction to a Decimal
Follow these steps whenever you want to write a fraction as a decimal:
-
Simplify the fraction if possible.
Reducing the fraction first can make the division easier. As an example, ( \frac{6}{8} ) can be simplified to ( \frac{3}{4} ). -
Divide the numerator by the denominator.
Use a calculator, long division, or the denominator’s relationship to a power of ten. -
Write the answer using decimal notation.
Include a zero before the decimal point when the result is less than one, such as 0.625 rather than simply .625. -
Check the result.
You can multiply the decimal by the original denominator to confirm that it produces the numerator.
Example: Converting ( \frac{7}{8} ) to a Decimal
Use long division:
- (7 \div 8) gives 0 with a remainder of 7.
- Place a zero after the decimal point and bring down the remainder, making 70.
- (70 \div 8 = 8), with a remainder of 6.
- Bring down another zero, making 60.
- (60 \div 8 = 7), with a remainder of 4.
- Bring down another zero, making 40.
- (40 \div 8 = 5), with no remainder.
The result is:
[ \frac{7}{8} = 0.875 ]
You can check the answer by multiplying:
[ 0.875 \times 8 = 7 ]
Example: Converting ( \frac{3}{5} ) to a Decimal
Since 5 is half of 10, ( \frac{3}{5} ) is equivalent to ( \frac{6}{10} ). Therefore:
[ \frac{3}{5} = 0.6 ]
Another way to find the answer is to divide (3) by (5):
[ 3 \div 5 = 0.6 ]
Example: Converting ( \frac{1}{8} ) to a Decimal
Because 8 divides evenly into 1,000, rewrite the fraction with a denominator of 1,000:
[ \frac{1}{8} = \frac{125}{1,000} ]
The number 125 represents the same value as 125 thousandths, so:
[ \frac{125}{1,000} = 0.125 ]
Thus:
[ \boxed{\frac{1}{8
