Place value is the idea that the position of a digit in a number determines its value. In our base-10 system, each place is a power of 10.
Whole numbers: ones, tens, hundreds, thousands
In the left part of the decimal, each position represents a power of 10.
- Ones means the digit is worth its face value (x 1).
- Tens means digit x 10.
- Hundreds means digit x 100.
- Thousands means digit x 1000.
Example: The number 4,589 has 9 in the ones place, 8 in the tens place, 5 in the hundreds place, and 4 in the thousands place. Expanded form: 4,000 + 500 + 80 + 9.
Decimals: tenths, hundredths, thousandths
To the right of the decimal point, each place represents a fraction of ten.
- Tenths = digit × 1/10
- Hundredths = digit × 1/100
- Thousandths = digit × 1/1000
Example: 3.276 means 3 ones plus 2 tenths plus 7 hundredths plus 6 thousandths. Expanded: 3 + 0.2 + 0.07 + 0.006.
Practice steps
- Look at each digit and say its value based on its place (ones, tens, hundreds, etc.).
- Write the expanded form by adding the values of each place.
- Check by adding the parts back together.
Quick practice
Write the expanded form for 5,412 and identify the value of 7 in 7,304. Write 0.58 in expanded form.
Answers: 5,412 = 5,000 + 400 + 10 + 2; 7 in 7,304 is thousands (7,000); 0.58 = 0.5 + 0.08 (or 5 tenths + 8 hundredths).