Math · Numbers

Place Value & Number Sense

Every digit in a number has a job. Its place tells you its value — and once you see how it works, big numbers aren't scary at all.

Part 01

What Is Place Value?

In our number system, the position of a digit determines how much it's worth. The digit 5 can mean five, fifty, five hundred, or even five thousand — it all depends on where it sits.

Think of it like an address! 🏠

Just like each house on a street has a different address, each position in a number has a different name and value. Moving one spot to the left makes a digit worth 10 times more.

Here's a place value chart showing the number 385,247:

Hundred-Thousands Ten-Thousands Thousands Hundreds Tens Ones
3300,000 880,000 55,000 , 2200 440 77

Each digit's value equals the digit times the value of its position. The 8 in the ten-thousands place is worth 8 × 10,000 = 80,000.

Part 02

Building Numbers with Base-Ten Blocks

Base-ten blocks are a great way to see place value. A tiny cube is 1, a rod is 10, a flat is 100, and a big cube is 1,000.

The number 1,253 in blocks
1000
× 1
Thousands
100
× 2
Hundreds
10
× 5
Tens
1
× 3
Ones
1,000 + 200 + 50 + 3 = 1,253
Part 03

Expanded Form

Expanded form breaks a number apart to show the value of each digit. It's like taking the number apart and labeling every piece.

47,603 in expanded form
40,000 + 7,000 + 600 + 3
Notice the 0 in the tens place — it means there are no tens, so we skip it!

💡 Why Expanded Form Matters

Expanded form helps you understand what a number really means. It's also super useful when you start adding and subtracting big numbers — you can work with each place separately!

Part 04

Explore: Tap Any Digit

Click or tap any digit in the number below to see its place and value. Hit the button to get a new number!

Tap a digit to explore
← tap a digit above
Part 05

Multiplying & Dividing by 10

When you multiply by 10, every digit shifts one place to the left — it becomes worth 10 times more. When you divide by 10, every digit shifts one place to the right.

The Shifting Rule 🔀

Multiply by 10 → digits move left (number gets bigger). Divide by 10 → digits move right (number gets smaller). The digits stay the same — only their position changes!

Watch the digits shift
350
Start: 350
Part 06

Practice Time!

Test your place value skills with these problems. Answer each one, then check your work.

Problem 1

What is the value of the highlighted digit?

Problem 2

Write this number in expanded form

Type each place value, separated by + signs. Example: 3000 + 200 + 50 + 1

Problem 3

Part 07

Key Terms

Place Value

The value of a digit based on its position in a number. In 452, the 4 has a place value of 400.

Digit

Any of the symbols 0–9 used to write numbers.

Expanded Form

A way to write a number showing the value of each digit. Example: 2,350 = 2,000 + 300 + 50.

Standard Form

The usual way to write a number using digits. Example: 2,350.

Base-Ten System

Our number system, where each place is 10 times the value of the place to its right.

Period

A group of three digits separated by commas. The ones period has ones, tens, hundreds. The thousands period has thousands, ten-thousands, hundred-thousands.