Decimals are numbers that have a whole number part and a fractional part, separated by a dot called the decimal point. The decimal point is like a wall that separates the ones, tens, and hundreds from the tenths, hundredths, and thousandths.
The Decimal Point
The decimal point (.) separates the whole number from the fraction. The numbers to the left of the decimal point are whole numbers. The numbers to the right of the decimal point are parts of a whole.
When we write 0.5, the digit 0 is the whole number and 5 is the fractional part. When we write 2.75, the digit 2 is the whole number and 75 is the fractional part.
Tenths
Imagine a shape divided into 10 equal parts. One part is 101 of the whole. In decimal form, we write this as 0.1.
Look at the table below:
| Fraction | 101 | 102 | 103 | 104 | 105 | 106 | 107 | 108 | 109 |
|---|
| Decimal | 0.1 | 0.2 | 0.3 | 0.4 | 0.5 | 0.6 | 0.7 | 0.8 | 0.9 |
Each decimal place to the right of the decimal point is divided by 10.
Hundredths
Now imagine a shape divided into 100 equal parts. One part is 1001 of the whole. In decimal form, we write this as 0.01.
Here are more examples from the diagram:
- 1003=0.03
- 10012=0.12
- 10094=0.94
Thousandths
For even smaller parts, we use thousandths. One part out of 1000 is 10001, written as 0.001.
Examples:
- 10002=0.002
- 100014=0.014
- 1000127=0.127