Grades K–2
Place value
Every digit is worth something different depending on where it sits. Getting this secure first is what makes column addition, subtraction and rounding make sense later.
What place value means
In 347 the 3 means three hundreds, the 4 means four tens and the 7 means seven ones: 300 + 40 + 7. The digits are the same symbols as in 734, but the number is very different, because each place is worth ten times the place to its right.
Zero holds a place open. In 305 there are no tens, and without the zero the number would read 35.
Worked examples
Expanded form
Write each digit as the amount it is worth, then add the parts back together.
Comparing numbers
Start at the biggest place. Both have 4 hundreds; 7 tens beats 2 tens, so 472 > 427.
Ten more
Adding ten changes only the tens digit, unless it passes 9.
Ways to make it stick
Say it in parts
Read 347 as "three hundred forty-seven", then again as "3 hundreds, 4 tens, 7 ones".
Bundle in tens
Count real objects into groups of ten. The groups are the tens; whatever is left over is the ones.
Zero is a digit
Compare 305 and 35 side by side. The zero is what pushes the 3 into the hundreds.
Ten times bigger
Each place to the left is worth ten times more: 1 ten is 10 ones, 1 hundred is 10 tens.
A place value chart
Each digit goes in the column for the place it holds. An empty place below the biggest digit is written as 0.
| Number | Thousands | Hundreds | Tens | Ones | Expanded form |
|---|---|---|---|---|---|
| 4,582 | 4 | 5 | 8 | 2 | 4,000 + 500 + 80 + 2 |
| 1,036 | 1 | 0 | 3 | 6 | 1,000 + 30 + 6 |
| 709 | 7 | 0 | 9 | 700 + 9 | |
| 60 | 6 | 0 | 60 |
Practice questions
Work each one on paper first, then open the answer to check it.
- What is the value of the 6 in 462?
Answer
60 (six tens) - Write 500 + 30 + 8 as a number.
Answer
538 - Write 709 in expanded form.
Answer
700 + 9 - Which is greater, 381 or 318?
Answer
381: both have 3 hundreds, and 8 tens beats 1 ten. - What number is ten more than 495?
Answer
505 - What number is one hundred less than 1,240?
Answer
1,140 - How many tens are in 90?
Answer
9 - Write the number with 4 hundreds, 0 tens and 6 ones.
Answer
406 - What is the value of the 2 in 2,315?
Answer
2,000 - Put in order, smallest first: 56, 506, 65, 560.
Answer
56, 65, 506, 560
Common questions
- Why does place value matter so much?
- Column addition and subtraction, rounding and decimals all depend on it. A child who lines digits up by place, rather than by the edge of the number, avoids most early column errors.
- When do children learn the thousands place?
- Numbers to 1,000 are usually a grade 2 goal. Larger numbers follow in grades 3 and 4, once hundreds are secure.