Place value: learn and practice

Who this lesson is for

This place value lesson is for grade 3. Students read the hundreds, tens, and ones in a three-digit number, including a zero that holds a place. The practice link opens the hundreds skill. The lesson has one address, and the grade 3 hub is the only hub that links here.

What a digit is worth

A three-digit number is built from hundreds, tens, and ones. In 472 the 4 is worth 400, the 7 is worth 70, and the 2 is worth 2. The digit itself is not the value. The place decides the value. Moving a digit one place to the left makes it ten times as large, so a 4 in the tens place is 40 and a 4 in the hundreds place is 400.

A zero holds a place

In 305 the 0 means there are no tens. The number is 3 hundreds and 5 ones, which is 300 + 5. It is not 35. Leaving the zero out slides the 3 into the tens place and changes the number. The zero is not an invitation to skip a column. It keeps every other digit in the place its name claims.

Worked example 1: the hundreds digit

What is the value of the 4 in 472? The 4 sits in the hundreds place, so its value is 4 × 100 = 400. It is not worth 4, and it is not worth 40. Those are the ones place and the tens place. Expand the whole number to check: 400 + 70 + 2 = 472. The hundreds part is the 400, which matches the digit you were asked about.

Worked example 2: a zero in the tens place

Write the value of each digit in 305. The 3 means 3 hundreds, which is 300. The 0 means 0 tens, which is 0. The 5 means 5 ones, which is 5. Add them: 300 + 0 + 5 = 305. Reading 305 as thirty-five skips the hundreds place. The zero is what stops that reading, because it keeps a column between 3 and 5.

Worked example 3: build a number from places

Build the number with 2 hundreds, 6 tens, and 4 ones. Two hundreds is 200. Six tens is 60. Four ones is 4. The sum is 200 + 60 + 4 = 264, so the digits in order are 2, 6, and 4. If the tens were missing, the number would be 204, not 24. The middle digit has to be written even when someone is only thinking about hundreds and ones.

Checks before you leave the problem

Name the place before you name the value. Multiply by 100 for hundreds, by 10 for tens, and by 1 for ones. Add the three values and confirm that you get the original number back. Then practice the same hundreds skill on the board.

Common questions about place value

Why does the same digit mean different amounts?

The place changes the value. A 4 in the ones place is 4. A 4 in the tens place is 40. A 4 in the hundreds place is 400. The ink looks the same, and the worth does not.

What does a zero in the middle mean?

That place is empty, and the digits on either side stay where they are. 305 is three hundred five, not thirty-five. Erasing the zero changes both the look and the amount.

Is 250 the same as 25 tens?

Yes. 25 tens is 250, and 2 hundreds plus 5 tens is also 250. The expanded form 200 + 50 + 0 makes the three places visible, including the empty ones place.