Apply the examples with Decimal Place Lab Game. Check the worked steps below, then practice on your own.
Decimal place value chart
Each step to the right divides the place value by ten. The decimal point separates the ones column from the tenths column.
| Place | Value | Digit in 12.345678 |
|---|---|---|
| Tens | 10 | 1 |
| Ones | 1 | 2 |
| Tenths | 0.1 | 3 |
| Hundredths | 0.01 | 4 |
| Thousandths | 0.001 | 5 |
| Ten-thousandths | 0.0001 | 6 |
| Hundred-thousandths | 0.00001 | 7 |
| Millionths | 0.000001 | 8 |
Build a number from its place values
In 12.345, the value of each digit is 10 + 2 + 0.3 + 0.04 + 0.005. These parts add to 12.345. The 4 is in the hundredths column, so it contributes 0.04.
Compare 2.4, 2.04 and 2.004: the 4 moves right, and its value becomes one tenth as large at each move.
Why zero is important
In 5.006, the zeroes occupy the tenths and hundredths columns, while the 6 is in the thousandths column. Removing those zeros to make 5.6 would change the number.
A trailing zero behaves differently: 5.600 and 5.6 are numerically equal, though a measurement may intentionally show three decimal places.
Compare decimal numbers correctly
Line up decimal points and, when useful, add trailing zeros: 0.7 = 0.70. Now 0.70 is visibly greater than 0.65. The number with more digits after the decimal point is not necessarily greater.
With negative decimals, −0.2 is greater than −0.9 because it lies closer to zero on the number line.
Place value and rounding
To round 6.384 to the nearest hundredth, look at the thousandths digit (4). Since 4 is below 5, the hundredths digit remains 8, giving 6.38.
To round to the nearest tenth, look at the hundredths digit (8), which rounds 6.384 to 6.4.
Quick practice questions
- In 4.072, what is the value of 7? Seven hundredths (0.07).
- Which is larger, 0.508 or 0.58? 0.58 (or 0.580).
- Write nine thousandths as a decimal. 0.009.
- Which place is the 6 in 1.000006? Millionths.
Test yourself with the Decimal Place Lab Game, then review any missed columns using this chart.
Frequently asked questions
What is the first decimal place?
The tenths place, worth one tenth or 0.1.
What is the sixth decimal place?
The millionths place, worth one millionth or 0.000001.
Why is 0.7 greater than 0.65?
Write 0.7 as 0.70; 70 hundredths is greater than 65 hundredths.
Open the Decimal Place Lab Game, then explore Decimals Quiz for more practice.