Why each place is worth ten times the next
In 4th grade, children learn that each place in a number is worth ten times the place to its right, so the 7 in 700 is ten times the 7 in 70.
By Robert “Bobby” BarnettMath teacher, parent, and founder of Bobby’s Math Club
Try these with your child
These are real questions from our 4th grade practice. Tap the speaker to hear one read aloud, or the light bulb for a hint, and talk about the answer together.
Question 1 of 3
Compare 40 thousands and 4 ten thousands. Which is true?
- 4 ten thousands is more
- They are equal
- 40 thousands is more
Why this matters
Seeing why each place is worth ten times the next gives your child the reason behind multiplying and dividing by 10, 100, and 1,000, from working out 30 × 40 in their head to turning meters into centimeters. In 5th grade it extends to decimals, where each place to the right is one tenth of the one before, so 0.7 is ten times 0.07. Without it, decimals tend to feel like a separate set of rules.
Where kids can get stuck
- Saying the 3 in 3,000 and the 3 in 300 are worth the same, without looking at their places.
- Seeing 500 as 450 more than 50 but not as ten times 50, because they think each place adds rather than multiplies.
- Using "multiply by 10, add a zero" as a trick, without being able to explain why 60 × 10 = 600.
How you can help
- Use play money or real coins: show that 10 dimes equal 1 dollar and 10 dollars equal a ten-dollar bill. Ask your child how many dimes would match $10, and talk through why it is 100.
- Point out a number with a repeated digit on a sign or receipt, such as 4,440. Ask your child what each 4 is worth and how many times bigger each is than the one to its right.
- Count by tens together while stacking cups or blocks: 10, 20, up to 100. Then ask how many hundreds would make a thousand, and have them say why it is 10.
For more, Bobby's Math Club has free practice at your child’s level.
Questions parents ask
Why is my child learning place value this way?
Seeing each place as ten times the place to its right gives your child the reason behind patterns they have noticed, like 40 × 10 = 400. Without the reason, children rely on rules such as "add a zero," which break later with decimals. Teachers often use blocks or place-value charts to show ten ones becoming a ten, and ten tens becoming a hundred.
Isn't multiplying by 10 the same as adding a zero?
For whole numbers it looks that way: 35 × 10 = 350. But the real reason is that every digit moves one place to the left, so each is worth ten times as much. That explanation keeps working in 5th grade with decimals, where 0.3 × 10 = 3. The "add a zero" shortcut would give 0.30, which is wrong, so teachers focus on the reason instead.
How can I tell if my child really understands this?
Ask a question that needs the idea rather than a memorized rule. For example, "How many tens are in 600?" A child who understands will say 60, and may explain that each hundred is ten tens. Or ask, "In 5,550, how does the 5 in the thousands place compare to the 5 in the hundreds place?" The answer is ten times as much.
Make learning math fun
Bobby's Math Club turns 4th grade math practice into something fun to do together.
- Unlimited practice, completely free
- Practice that starts where your child is and grows with them
- You see their progress and what to work on next
Written by Robert “Bobby” Barnett
Bobby is an award-winning math teacher, the author of Meet Every Learner’s Needs, and the father of two elementary-school math learners. He uses Bobby’s Math Club with his own kids a few times every week. Learn more or contact Bobby.
Ready to watch your child’s confidence grow?
Your 4th grade child can start today with free, unlimited practice that grows with them.
Join the clubNote for teachers: This skill is covered by Common Core math standard 4.NBT.A.1: “Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division.” Learn how Bobby's Math Club can help your students grow. (Common Core 4.NBT.1)