Decimal Fraction — Definition, Formula & Examples
A decimal fraction is a fraction that has a power of 10 as its denominator, such as 10, 100, or 1000. Numbers like , , and are all decimal fractions.
A decimal fraction is any rational number that can be expressed as a fraction , where is an integer and is a positive integer. Every decimal fraction has an exact finite decimal representation.
How It Works
Decimal fractions are the bridge between fractions and decimals. The denominator tells you which decimal place to use: 10 means tenths, 100 means hundredths, 1000 means thousandths. To convert a decimal fraction to decimal notation, simply count the zeros in the denominator — that tells you how many digits go after the decimal point. For example, becomes because 100 has two zeros, so you need two decimal places.
Worked Example
Problem: Write as a decimal.
Step 1: Count the zeros in the denominator. 1000 has three zeros, so the decimal will have three places after the decimal point.
Step 2: Write the numerator 25 so it fills three decimal places. Place a zero in front to reach three digits.
Answer:
Why It Matters
Decimal fractions are how money works: \ is really . Understanding this connection helps you switch between fractions and decimals when solving problems involving measurement, money, and percentages.
Common Mistakes
Mistake: Forgetting to include leading zeros when converting to a decimal. For instance, writing as instead of .
Correction: Always match the number of decimal places to the number of zeros in the denominator. Since 100 has two zeros, you need two digits after the decimal point: .