What Is a Decimal?
A decimal is a number that uses a decimal point to show values less than one (or values between whole numbers).
In 3.75:
- 3 = three ones (whole number part)
- .7 = seven tenths
- .05 = five hundredths
So 3.75 = 3 + 7/10 + 5/100 = 3 + 75/100 = 3 3/4.
Decimals are fractions
Every decimal is a fraction with a denominator that is a power of 10:
| Decimal | Fraction | In words |
|---|---|---|
| 0.1 | 1/10 | one tenth |
| 0.25 | 25/100 = 1/4 | twenty-five hundredths |
| 0.5 | 5/10 = 1/2 | five tenths |
| 0.75 | 75/100 = 3/4 | seventy-five hundredths |
| 0.333... | 1/3 | one third (repeating) |
The decimal point
The decimal point separates the whole number part from the fractional part. Everything to the left is whole units. Everything to the right is parts of a unit.
Each place to the right of the decimal is 10 times smaller:
- Tenths (0.1) → Hundredths (0.01) → Thousandths (0.001)
This is the same place value pattern as whole numbers, extended past the ones place.
Decimals and money
Money is the most familiar decimal system:
- $1.00 = 1 dollar
- $0.10 = 1 dime = 1 tenth of a dollar
- $0.01 = 1 penny = 1 hundredth of a dollar
$3.75 = 3 dollars, 7 dimes, and 5 pennies.
Related concepts
- How to Teach Decimals: full teaching guide
- Decimal place value: extending place value
- Decimal operations: add, subtract, multiply, divide
- Percents: decimals, fractions, and percents are three forms of the same value