Decimal Place Value – Tenths, Hundredths, and Thousandths
You already know about place value in whole numbers — hundreds, tens, and ones. Decimal place value extends that idea to the right of the decimal point, giving us tenths, hundredths, thousandths, and beyond.
This symmetry around the ones place — tens and tenths, hundreds and hundredths — is a direct consequence of the base-10 (decimal) number system the whole scheme is built on: each column, in either direction, is exactly ten times its neighbour. Precision instruments make heavy use of these small columns: a digital kitchen scale reading grams to one decimal place is working in tenths, while a laboratory balance or a GPS coordinate might rely on thousandths or beyond. Losing track of which column a digit sits in is one of the most common sources of real-world measurement error, which is exactly why place-value fluency matters well past the classroom.
The Place Value Chart
| Thousands | Hundreds | Tens | Ones | . | Tenths | Hundredths | Thousandths |
|---|---|---|---|---|---|---|---|
| 1,000 | 100 | 10 | 1 | . | 1/10 | 1/100 | 1/1000 |
Each column is ten times the value of the column to its right, just as with whole numbers.
Reading a Decimal Using Place Value
4 is in the ones place.
3 is in the tenths place (3/10).
7 is in the hundredths place (7/100).
2 is in the thousandths place (2/1000).
The number means: 4 + 3/10 + 7/100 + 2/1000.
0 is in the ones place.
0 is in the tenths place — this zero is a placeholder.
5 is in the hundredths place.
6 is in the thousandths place.
This number means 56 thousandths.
Why Placeholders Matter
In 0.056, the zero in the tenths place is a placeholder. Without it, writing 0.56 would mean something completely different — 56 hundredths, which is ten times larger.
Expanded Form
| Number | Expanded Form |
|---|---|
| 3.4 | 3 + 4/10 |
| 12.75 | 10 + 2 + 7/10 + 5/100 |
| 0.308 | 3/10 + 8/1000 |
| 5.029 | 5 + 2/100 + 9/1000 |
What Each Digit is Worth
7 is in the hundredths column. Its value is 7/100 = 0.07.
5 is in the thousandths column. Its value is 5/1000 = 0.005.
Multiplying and Dividing by Powers of 10
| Operation | Effect on Digits | Example |
|---|---|---|
| Times 10 | Digits shift one place left | 2.34 x 10 = 23.4 |
| Times 100 | Digits shift two places left | 2.34 x 100 = 234 |
| Divide by 10 | Digits shift one place right | 45.6 / 10 = 4.56 |
| Divide by 100 | Digits shift two places right | 45.6 / 100 = 0.456 |
Key Takeaways
- The decimal point is a fixed marker; the digits move around it.
- Tenths are 10 times smaller than ones; hundredths are 10 times smaller than tenths.
- Zero placeholders are essential — never drop them unless they are trailing zeros.
- Multiplying by 10 shifts digits left; dividing by 10 shifts them right.