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 $3{,}456{,}789$ is read as "three million, four hundred fifty-six thousand, seven hundred eighty-nine." 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: $3{,}000{,}000 + 400{,}000 + 50{,}000 + 6{,}000 + 700 + 80 + 9$

In expanded form, each digit keeps its place value. The 4 is really $400{,}000$ because it sits in the hundred thousands place, not just a plain "4."

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 → $2{,}000{,}000$
• 0 ten thousands → adds nothing, so we skip it
• 7 is in the ten thousands place → $70{,}000$
• 5 is in the thousands place → $5{,}000$
• 3 is in the hundreds place → $300$

Step 3 — Add the values together. $2{,}000{,}000 + 70{,}000 + 5{,}000 + 300$

We leave out the zeros because they add nothing to the total.

Worked Example: Standard Form → Word Form 🗣️

Now let's write $618{,}042$ in word form.

Step 1 — Split at the comma into groups.

• The first group is 618 → "six hundred eighteen"
• The comma after it means thousand
• The last group is 042, which is just 42 → "forty-two"

Step 2 — Put it together, saying the group name at each comma.

six hundred eighteen thousand, forty-two

Notice we do not say "zero" for the 0 in the hundreds place of the last group. We just read $042$ as "forty-two." Now try filling in the boxes below!

Your Turn: Fill in the Blanks ✍️

Look at the number $5{,}340{,}000$.

1. Write the digit that is in the millions place.
2. Write the value of the digit $3$ (it is in the hundred thousands place). Type it as a plain number with no commas, like $300000$.
3. In the number $720{,}000$, write the digit in the ten thousands place.

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	Read As
$80{,}000$	eighty thousand
$1{,}250{,}000$	one million, two hundred fifty thousand
$3{,}600{,}000$	three million, six hundred thousand

Let's use a real-world number in the problem below.

Word Problem: City Population 🏙️

A city's population is two million, four hundred eight thousand, sixty people.

1. Write this number in standard form with commas, like $2{,}408{,}060$.
2. What digit is in the millions place of this number?
3. What is the value of the digit $4$ in this number? Type it as a plain number with no commas, like $400000$.

Apply What You Know ✅

Use comparing-by-place-value to answer this real-world question.

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
Expanded form	Each digit's value added up	$3{,}000{,}000 + 400{,}000 + 50{,}000 + 6{,}000 + 700 + 80 + 9$
Comparing	Compare digits left to right	$5{,}234{,}567 > 5{,}198{,}432$

Remember: to compare two numbers, start at the biggest place on the left and move right until the digits are different. The first number with the bigger digit is the greater number.

Challenge: Mix It All Up 🚀

These questions mix together everything from the lesson. Take your time!