Extending place value
You know that each place is worth ten times the place to its right. Decimals continue the pattern to the right of the ones place, where each place is worth one tenth of the place to its left.
| Tens | Ones | . | Tenths | Hundredths | Thousandths |
|---|---|---|---|---|---|
| 10 | 1 | . | 1/10 | 1/100 | 1/1,000 |
| 3 | . | 4 | 7 | 2 |
The number 3.472 means 3 ones, 4 tenths, 7 hundredths and 2 thousandths.
The decimal point
The decimal point separates whole numbers from parts of a whole. Everything left of it is 1 or more; everything right is less than 1.
Values of decimal digits
In 5.386:
| Digit | Place | Value |
|---|---|---|
| 5 | ones | 5 |
| 3 | tenths | 0.3 = 3/10 |
| 8 | hundredths | 0.08 = 8/100 |
| 6 | thousandths | 0.006 = 6/1,000 |
Expanded form: 5 + 0.3 + 0.08 + 0.006.
Picturing decimals
Imagine a square split into 100 small squares (a hundred grid):
- One column of 10 small squares = 1 tenth = 0.1
- One small square = 1 hundredth = 0.01
- 0.35 = 3 columns and 5 small squares = 35 of the 100 squares
Money is another great model:
- $1.00 = 1 dollar
- $0.10 = 1 dime = one tenth of a dollar
- $0.01 = 1 cent = one hundredth of a dollar
Zeros in decimals
- Zeros at the end after the decimal point don’t change the value: 0.5 = 0.50 = 0.500.
- Zeros in the middle are placeholders and do matter: 0.05 is very different from 0.5.
Worked examples
Example 1: What is the value of the 7 in 2.374?
It’s in the hundredths place: 0.07 (7/100).
Example 2: Write 4 + 0.6 + 0.009 as a decimal.
There are no hundredths, so use a 0: 4.609.
Example 3: How many hundredths are in 0.4?
0.4 = 0.40 = 40 hundredths.
Common mistakes
- Thinking the first place after the point is "oneths". It’s tenths.
- Forgetting placeholder zeros: writing 4 + 0.6 + 0.009 as 4.69.
- Thinking 0.25 is bigger than 0.3 because 25 > 3. Compare tenths first.
Try it yourself
- What is the value of the 3 in 6.135?
- Write 8 + 0.2 + 0.05 as a decimal.
- Which digit is in the thousandths place in 9.8146?
- Write 0.73 in expanded form.
Answers: 1) 0.03 2) 8.25 3) 4 4) 0.7 + 0.03
Quick recap
- Decimals extend place value to the right of the decimal point.
- Places: tenths, hundredths, thousandths, each ten times smaller.
- Zeros in the middle are placeholders; zeros at the end don’t change the value.