Place Value with Large Numbers

What Is Place Value? 🔢

Every digit in a number has a special job. The job a digit does depends on where it sits. This idea is called place value.

Look at the digit 5 in two different numbers:

• In $50$, the 5 means 5 tens, which is $50$.
• In $500$, the 5 means 5 hundreds, which is $500$.

The digit is the same, but its position changes its value! As you move left, each place is 10 times bigger than the place to its right.

The places, from right to left, are:

• ones, tens, hundreds
• thousands, ten thousands, hundred thousands
• millions

Reading a Big Number 📊

Let's break apart the number $3{,}456{,}789$ using a place value chart.

Millions	Hundred Thousands	Ten Thousands	Thousands	Hundreds	Tens	Ones
3	4	5	6	7	8	9

We use commas to split big numbers into groups of three. Reading from left to right:

• 3 is in the millions place → 3 million
• 456 are the next three digits → 456 thousand
• 789 are the last three digits → 789

So $$ is read as Notice how each comma helps you say the group name (million, thousand) out loud.

Three Ways to Write a Number ✍️

The same number can be written three different ways. They all mean exactly the same thing!

1. Standard Form — the regular way we write numbers: $3{,}456{,}789$

2. Word Form — the number written in words: three million, four hundred fifty-six thousand, seven hundred eighty-nine

3. Expanded Form — showing the value of each digit added together: $3{,}000{,}000 + 400{,}000 + 50{,}000 + 6{,}000 + 700 + 80 + 9$

Quick Concept Check ✅

You just learned how place value gives each digit its value. Let's make sure it stuck!

Worked Example: Standard Form → Expanded Form 🛠️

Let's write $2{,}075{,}300$ in expanded form, one place at a time.

Step 1 — Make a place value chart.

Millions	Hundred Thousands	Ten Thousands	Thousands	Hundreds	Tens	Ones
2	0	7	5	3	0	0

Step 2 — Find the value of each non-zero digit.

• 2 is in the millions place → $2{,}000{,}000$

Guided Practice: Choose the Best Answer 🧠

Read each question carefully and pick the correct choice.

Guided Practice: Name the Place 🔽

For each number, choose the correct place that the bold digit sits in.

Big Numbers in Real Life 🌎

Large numbers are everywhere once you start looking!

• A big sports stadium might hold about $80{,}000$ fans.
• A medium-sized city might have a population of $1{,}250{,}000$ people.
• A popular video might get $3{,}600{,}000$ views.

When you read these numbers, the commas do the hard work for you. The comma group on the far left tells you how many millions, the next group tells you how many thousands, and the last group is the leftover hundreds, tens, and ones.

Number

Review: Putting It All Together 🏁

Great work! Here is a quick summary of everything you learned about large numbers.

Idea	What It Means	Example
Place value	A digit's value depends on its position	The 6 in $6{,}000{,}000$ means six million
Standard form	The regular number with commas	$3{,}456{,}789$
Word form	The number written in words	three million, four hundred fifty-six thousand, seven hundred eighty-nine