Ones, Tens, and Hundreds

Learn how digits in different positions represent different values in our number system.

Elementary15 minLesson
Printable worksheet

Definition

Place value tells us how much a digit is worth based on its position in a number.
In our number system, each position has a value 10 times greater than the position to its right:
PositionValueExample in 253
Hundreds1002 hundreds = 2×100=2002 \times 100 = 200
Tens105 tens = 5×10=505 \times 10 = 50
Ones13 ones = 3×1=33 \times 1 = 3
So 253=200+50+3253 = 200 + 50 + 3
This is called expanded form - writing a number as the sum of the values of each digit.

Try it now

In the number 345, which digit is in the tens place?

Worked Examples

What is the value of each digit in 472?
1

Identify the ones digit

The rightmost digit is 2 → 2×1=22 \times 1 = 2
2

Identify the tens digit

The middle digit is 7 → 7×10=707 \times 10 = 70
3

Identify the hundreds digit

The leftmost digit is 4 → 4×100=4004 \times 100 = 400
4

Write in expanded form

Add all values together → 472=400+70+2472 = 400 + 70 + 2

Common Mistakes

Confusing the digit with its value (saying the 5 in 350 is worth 5)

Why it's wrong: The position matters! The 5 is in the tens place, so it represents 50, not 5.

Correct: Always multiply the digit by its place value: 5×10=505 \times 10 = 50

Forgetting zero as a placeholder (writing 608 as 68)

Why it's wrong: Zero holds the position. Without the 0, the 6 would move to the tens place.

Correct: 608 means 6 hundreds, 0 tens, 8 ones. The zero keeps 6 in the hundreds place.

Interactive Visual

Place Value Chart

Enter a number:

253
Hundreds
100
Tens
10
Ones
1
253

Expanded Form:

2 × 100 + 5 × 10 + 3 × 1

Click on any place value to highlight it and see its value.

Interactive Sandbox

Expression Calculator

Try these:

History

No calculations yet

Practice Problems

16 problems
Problem 1 of 16
Easy
In the number 345, which digit is in the tens place?

Why It Matters

Understanding place value is the foundation of all math!
  • Reading numbers: When you see 847, you know it means "eight hundred forty-seven"
  • Adding and carrying: When adding 58 + 37, you need to know that 5 and 3 are in the tens place
  • Money: A 100 dollar bill is worth ten 10 dollar bills, which is worth one hundred 1 dollar bills
  • Measurement: 1 meter = 10 decimeters = 100 centimeters
Without place value, we would need a different symbol for every number - imagine memorizing millions of symbols!

Real World Applications

Money and Bills

Our money system uses place value! A 100 dollar bill equals ten 10 dollar bills or one hundred 1 dollar bills.

Example:

If you have 3 hundred dollar bills, 2 ten dollar bills, and 7 one dollar bills, you have 327 dollars total.

1Try It Yourself

You have 4 hundred dollar bills, 5 ten dollar bills, and 6 one dollar bills.

How much money do you have in total?

Step 1: Write the mathematical expression

Calculate the total:

Addresses and House Numbers

House numbers are written with place value too. In house number 253, the 2 means 2 hundreds, the 5 means 5 tens and the 3 means 3 ones.

Example:

Houses 253 and 235 use the same three digits, but they are different houses: in 253 the 5 is worth 50, in 235 it is worth only 5.

2Try It Yourself

A house number is 5 hundreds, 0 tens, and 9 ones.

What is the house number?

Step 1: Write the mathematical expression

Find the house number:

Key Takeaways

  • 1Each position in a number has a value: ones (1), tens (10), hundreds (100)
  • 2The value of a digit equals the digit times its place value
  • 3Expanded form shows a number as the sum of each digit's value: 253=200+50+3253 = 200 + 50 + 3
  • 4Zero is a placeholder that keeps other digits in their correct positions

Frequently Asked Questions

Zero holds the tens place. Without it, 305 would become 35, which is a completely different number! Zero tells us there are no tens, but it keeps the 3 in the hundreds position.
Zero holds the tens place. Without it, 305 would become 35, which is a completely different number! Zero tells us there are no tens, but it keeps the 3 in the hundreds position.
Because each place is worth 10 times more than the place to its right. We use 10 digits (0-9), and when we count past 9, we move to the next place. This is probably because humans have 10 fingers!

Glossary

Place value
The value of a digit based on its position in a number
Digit
A single symbol used to write numbers (0, 1, 2, 3, 4, 5, 6, 7, 8, 9)
Expanded form
A number written as the sum of each digit's value (e.g., 253=200+50+3253 = 200 + 50 + 3)
Placeholder
A zero that holds a position when there are no units of that value
Today's challengeOne problem, three tries

More in This Topic

Introduction to Place Value

Elementary20 min

Expanded Form

Elementary15 min

Comparing Whole Numbers

Elementary15 min

Ordering Whole Numbers

Elementary20 min