Place Value

For Elementary Students

What Is Place Value?

Place value means that a digit's value depends on where it sits in a number.

Think about it like this: The number 3 can mean 3, 30, 300, or even 3,000 — all depending on its position!

The Same Digit, Different Values

Look at the number 222:

• The first 2 (from the left) means 200 (two hundred)
• The middle 2 means 20 (twenty)
• The last 2 means 2 (two)

Same digit, but each has a different value because of where it is!

Understanding Place Value with Base-10 Blocks

Imagine building with blocks:

• 1 small cube = 1 (one)
• 1 stick of 10 cubes = 10 (ten)
• 1 flat square of 100 cubes = 100 (one hundred)
• 1 big cube of 1,000 cubes = 1,000 (one thousand)

The number 235 would be:

• 2 hundred-flats (200)
• 3 ten-sticks (30)
• 5 one-cubes (5)

The Places (From Right to Left)

Starting from the right side and moving left:

Example: 4,582

4    ,    5    8    2
↓         ↓    ↓    ↓
Thousands Hundreds Tens Ones

• 2 is in the ones place → 2
• 8 is in the tens place → 80
• 5 is in the hundreds place → 500
• 4 is in the thousands place → 4,000

Total: 4,000 + 500 + 80 + 2 = 4,582

Why Does This Matter?

If you know place value, you can:

• Read big numbers
• Compare numbers ("Is 543 bigger than 534?")
• Add and subtract correctly
• Understand what each digit means

The Role of Zero

Zero is a special placeholder. It means "nothing in this place."

Example: Look at 305

• 3 is in the hundreds place (300)
• 0 is in the tens place (no tens!)
• 5 is in the ones place (5)

Without the zero: If we wrote 35 instead, it would mean thirty-five, not three hundred five!

Zero holds the spot so we know there are no tens.

For Junior High Students

Place Value Chart

Here's how place value works from right to left:

So: 6,742 = 6,000 + 700 + 40 + 2

Standard Form, Expanded Form, and Word Form

Standard form: The regular way we write numbers

• 3,456

Expanded form: Writing the value of each digit

• 3,000 + 400 + 50 + 6

Word form: Writing the number in words

• "Three thousand, four hundred fifty-six"

More Examples

Number: 8,027

• Standard form: 8,027
• Expanded form: 8,000 + 0 + 20 + 7 (or just 8,000 + 20 + 7)
• Word form: Eight thousand, twenty-seven

Number: 50,309

• Standard form: 50,309
• Expanded form: 50,000 + 0 + 300 + 0 + 9 (or 50,000 + 300 + 9)
• Word form: Fifty thousand, three hundred nine

Larger Place Values

The pattern continues beyond thousands:

Example: 3,462,815

Reading from left to right:

• 3 millions = 3,000,000
• 4 hundred thousands = 400,000
• 6 ten thousands = 60,000
• 2 thousands = 2,000
• 8 hundreds = 800
• 1 ten = 10
• 5 ones = 5

Using Commas

Commas help us read large numbers by grouping digits into sets of three from right to left.

Example: 1234567

With commas: 1,234,567

Read as: "One million, two hundred thirty-four thousand, five hundred sixty-seven"

Comparing Numbers Using Place Value

To compare two numbers, look at digits from left to right:

Example: Compare 4,536 and 4,589

• Thousands place: both have 4 (same)
• Hundreds place: both have 5 (same)
• Tens place: 3 vs 8 → 8 is bigger!

Answer: 4,589 > 4,536

Multiplying and Dividing by 10, 100, 1,000

Pattern for multiplying: Move digits to the left (add zeros)

• 25 × 10 = 250 (each digit moves one place left)
• 25 × 100 = 2,500 (two places left)
• 25 × 1,000 = 25,000 (three places left)

Pattern for dividing: Move digits to the right

• 250 ÷ 10 = 25
• 2,500 ÷ 100 = 25
• 25,000 ÷ 1,000 = 25

Real-Life Uses

Money: $5,432 = 5 thousands + 4 hundreds + 3 tens + 2 ones

Population: City has 245,781 people

Distance: Trip is 1,056 miles

Scores: Video game score: 98,450 points

Practice