Click image to open full size
Math
Place Value
Building Numbers with Ones Tens Hundreds and Thousands
Related Tools
Related Labs
Related Worksheets
Related Cheat Sheets
Place value is the system we use to build and read numbers by grouping digits into ones, tens, hundreds, and thousands. Each place in a number has a value based on its position. This matters because the digit 4 can mean 4 ones, 4 tens, 4 hundreds, or 4 thousands depending on where it is. Place value helps students compare numbers, write numbers in different forms, and understand addition and subtraction.
Key Facts
- 10 ones = 1 ten
- 10 tens = 1 hundred
- 10 hundreds = 1 thousand
- In 3,482, the digit 3 means 3 thousands, the digit 4 means 4 hundreds, the digit 8 means 8 tens, and the digit 2 means 2 ones.
- Expanded form shows the value of each digit: 3,482 = 3,000 + 400 + 80 + 2
- A zero in a place holds that place: 2,057 = 2,000 + 0 hundreds + 50 + 7
Vocabulary
- Place value
- Place value is the value of a digit based on its position in a number.
- Ones
- Ones are single units used to count from 0 to 9 in the ones place.
- Tens
- Tens are groups of 10 ones and are shown in the tens place.
- Hundreds
- Hundreds are groups of 100 ones or 10 tens and are shown in the hundreds place.
- Thousands
- Thousands are groups of 1,000 ones or 10 hundreds and are shown in the thousands place.
Common Mistakes to Avoid
- Reading each digit as a separate number is wrong because 4,215 is not just 4, 2, 1, and 5. Each digit has a place value, so it means 4,000 + 200 + 10 + 5.
- Ignoring zeros is wrong because zeros can hold an important place in a number. In 3,008, the zeros show that there are no hundreds or tens.
- Mixing up tens and hundreds is wrong because 6 tens means 60, while 6 hundreds means 600. Always check the column before naming the value.
- Writing expanded form without place values is wrong because 5,732 is not 5 + 7 + 3 + 2. The correct expanded form is 5,000 + 700 + 30 + 2.
Practice Questions
- 1 Write 6,438 in expanded form.
- 2 A number has 2 thousands, 5 hundreds, 0 tens, and 9 ones. What is the number?
- 3 Explain why the digit 7 has a different value in 7,312 and 3,712.