What is a Decimal?
A decimal is a number that represents a part of a whole.
Decimals are separated by a decimal point.
Example:
3.5
The decimal point separates:
- whole numbers on the left
- parts of a whole on the right
Decimals are based on place value, just like whole numbers.
Understanding the Decimal Point
The decimal point is very important because it tells us where the whole number ends and where the fractional part begins.
Example:
4.2
- 4 is the whole number
- 2 represents tenths
This means:
4 wholes and 2 tenths
Decimal Place Value
Each place after the decimal point becomes smaller by ten.
| Place Value | Example |
|---|---|
| Ones | 5 |
| Tenths | 0.5 |
| Hundredths | 0.05 |
| Thousandths | 0.005 |
Understanding Tenths
Tenths are created when a whole is divided into 10 equal parts.
Example:
0.7
This means:
7 tenths
Fraction form:
7/10
Understanding Hundredths
Hundredths are created when a whole is divided into 100 equal parts.
Example:
0.25
This means:
25 hundredths
Fraction form:
25/100
Reading Decimals
Decimals are read by saying:
- the whole number
- the word “and”
- the decimal part
Examples:
| Decimal | Read As |
|---|---|
| 2.5 | Two and five tenths |
| 0.8 | Eight tenths |
| 1.25 | One and twenty-five hundredths |
| 3.04 | Three and four hundredths |
Comparing Decimals
When comparing decimals:
- Compare the whole numbers first.
- If the whole numbers are equal, compare the digits after the decimal point.
Example:
0.7 > 0.5
Because 7 tenths is greater than 5 tenths.
Decimals and Money
Money is one of the most common real-life uses of decimals.
Example:
- $1.50 means 1 dollar and 50 cents
- $2.75 means 2 dollars and 75 cents
Decimals help us calculate prices, savings, and change.
Decimals and Fractions
Decimals and fractions represent the same idea: parts of a whole.
| Fraction | Decimal |
|---|---|
| 1/2 | 0.5 |
| 1/4 | 0.25 |
| 3/4 | 0.75 |
| 1/10 | 0.1 |