Comparing Two Three-Digit Numbers - 2nd Grade Math

Section 1

Why Do We Compare Numbers?

Have you ever wanted to know who scored more points in a game? Or which bag of apples has more? People have been comparing amounts for a very, very long time! Let's take a quick peek at how comparing numbers started.

Long, Long Ago

Early people used pebbles and sticks to keep track of things like sheep. They would line up pebbles to see which group had more.

Ancient Egypt

The Egyptians wrote numbers using pictures called hieroglyphs. They could compare big numbers by looking at which picture symbols showed more.

India & Arabia

People in India invented the digits 0 through 9 that we use today. They also invented place value, which means each spot in a number means something different!

About 1600s

A mathematician named Thomas Harriot started using the symbols > and < to show which number is greater or less. We still use them today!

Today, you will learn how to compare three-digit numbers like 347 and 285. The secret is to understand what each digit is worth. That's called place value. Ready? Let's go!

Section 2

Big Ideas You Need to Know

Before we start comparing, let's learn four important ideas. These are your tools for comparing any three-digit numbers!

Place Value

In a three-digit number, each digit has its own spot. The first digit tells you hundreds, the second digit tells you tens, and the third digit tells you ones.

Hundreds Are the Biggest

The hundreds place is worth the most. One hundred is bigger than any number of tens or ones you can have in a three-digit number. So always look at hundreds first!

Tens Come Next

If the hundreds digits are the same, look at the tens next. Ten is bigger than any number of ones you can have. The tens digit helps you decide!

Ones Break a Tie

If hundreds and tens are both the same, then look at the ones place. That last digit will tell you which number is bigger — or if they are equal!

✦

Key Takeaway

Think of a three-digit number like a stack of blocks. Hundreds are big flat squares (worth 100 each). Tens are long sticks (worth 10 each). Ones are tiny cubes (worth 1 each). When you compare two stacks, always look at the big flat squares first. If they have the same number of big squares, then look at the sticks. If the sticks are the same too, count the tiny cubes!

Section 3

See It! Place Value Blocks

Let's look at two numbers side by side: 352 and 317. We can use place value blocks to see them clearly.

Look at the picture above! Both numbers have 3 hundreds. That's a tie so far. But 352 has 5 tens, while 317 only has 1 ten. Five tens is way more than one ten! So 352 is greater than 317. We don't even need to check the ones!

Section 4

How to Compare Step by Step

Here are the three steps you follow every time you compare two three-digit numbers. It's like a little recipe!

Step 1 — Compare the Hundreds

Look at the FIRST digit of each number.

If one has MORE hundreds, that number is GREATER. You're done! If they have the SAME hundreds, go to Step 2.

Step 2 — Compare the Tens

Look at the SECOND digit of each number.

If one has MORE tens, that number is GREATER. You're done! If they have the SAME tens, go to Step 3.

Step 3 — Compare the Ones

Look at the THIRD digit of each number.

If one has MORE ones, that number is GREATER. If they have the SAME ones, the two numbers are EQUAL!

Always start from the left and work to the right. The hundreds are the most important because they stand for the biggest amount. A single extra hundred is worth more than nine extra tens!

The Comparison Symbols

> means "is greater than" < means "is less than" = means "is equal to"

A fun trick: the symbol always opens its "mouth" toward the BIGGER number, like a hungry alligator! 🐊

Section 5

Place Value Chart — Break the Numbers Apart

A place value chart helps you see every digit lined up. It makes comparing super easy! Let's look at a few pairs of numbers in a chart.

See how it works? In Pair 1, the hundreds are the same (both 5), so we look at tens. Eight tens beats three tens, so 582 > 539. In Pair 2, hundreds are the same AND tens are the same, so we look at ones. One is less than eight, so 471 < 478. In Pair 3, every single digit is the same, so 256 = 256!

Section 6

Worked Example: Let's Do One Together!

Let's compare 648 and 672. Follow along!

Comparing 648 and 672

1
Step 1 — Look at the Hundreds

The first digit of 648 is 6. The first digit of 672 is 6. They are the same! Both numbers have 6 hundreds (that's 600). We need to keep going.
2
Step 2 — Look at the Tens

The second digit of 648 is 4. That means 4 tens, or 40. The second digit of 672 is 7. That means 7 tens, or 70. Is 4 the same as 7? No! 4 is less than 7.
3
Step 3 — We Can Stop!

Since the tens are different, we already know the answer. We don't need to check the ones! Four tens is less than seven tens.
4
Final Answer

648 is less than 672 because 4 tens is less than 7 tens.

648 < 672

Section 7

The Three Comparison Symbols

Here is a handy chart to help you remember the three symbols you use when comparing numbers.

Symbol	What It Means	Example	How to Remember
>	Greater than	583 > 491	The open (wide) side faces the bigger number. 🐊 The alligator eats the bigger one!
<	Less than	210 < 375	The pointy side points at the smaller number.
=	Equal to	444 = 444	Two even lines — both sides are the same!

✦

Key Takeaway

Think of the > and < symbols like a hungry alligator's mouth. The alligator always opens its mouth toward the bigger number because it wants to eat the most food! So if you write 583 > 491, the alligator's mouth is open toward 583 because that's the bigger meal. 🐊

Section 8

What Comes Next?

Great job learning to compare three-digit numbers! This skill will help you with even bigger numbers later on. Here's a peek at what's coming.

What You Know Now	What You'll Learn Later
Compare numbers up to 999	Compare numbers in the thousands (like 3,452 and 3,891) and even bigger!
Use >, <, and =	Put many numbers in order from least to greatest (or greatest to least)
Look at hundreds, tens, ones	Use place value to round numbers and estimate

The same steps you learned today — start at the biggest place and work your way right — work for any number, no matter how many digits it has! You are building a skill you will use forever. That's pretty awesome! 🌟

Section 9

Practice Problems

Now it's your turn! Try these five problems. Click "Show Answer" when you are ready to check your work.

Question 1: Problem 1 — What Does It Mean?

What does the symbol > mean? And which place do you check first when you compare two three-digit numbers?

Show answer

The symbol > means "is greater than." When you compare two three-digit numbers, you always check the hundreds place first because hundreds are worth the most. If the hundreds are the same, then you check tens, and then ones. Nice work if you got that!

Question 2: Problem 2 — Pick the Right Symbol

Fill in the blank with >, <, or =: 735 _____ 712

Show answer

The answer is 735 > 712. Here's how: Both numbers have 7 hundreds — that's a tie. Next, look at the tens. 735 has 3 tens and 712 has 1 ten. Three is more than one, so 735 is greater! You did it!

Question 3: Problem 3 — Two Numbers to Compare

Compare these two numbers. Write the correct symbol: 489 _____ 493

Show answer

The answer is 489 < 493. Both numbers have 4 hundreds — same! Now look at the tens. 489 has 8 tens and 493 has 9 tens. 8 is less than 9, so 489 < 493. Always double-check your digits!

Question 4: Problem 4 — Real-World Story

Maya's school collected 561 cans for a food drive. Jake's school collected 516 cans. Which school collected more cans? Use a symbol to show your answer.

Show answer

561 > 516, so Maya's school collected more cans! Both numbers have 5 hundreds. Next, 561 has 6 tens and 516 has 1 ten. Six tens (60) is way more than one ten (10). Maya's school wins! Great job solving a real-life problem! 🎉

Question 5: Problem 5 — Think About It!

Sam says: "I don't need to look at the tens or ones. I know that 892 is greater than 799." Is Sam right? Why or why not?

Show answer

Yes, Sam is right! 892 has 8 hundreds and 799 has 7 hundreds. Since 8 hundreds is more than 7 hundreds, 892 is definitely greater — no matter what the tens and ones are. Even though 799 has 9 tens and 9 ones, those can't add up to another hundred! This is why hundreds are the most important digit to check first. You are really thinking like a math star! ⭐

Summary

Lesson Recap

Summary

In this lesson, you learned how to compare two three-digit numbers by looking at place value. Every three-digit number is made of hundreds, tens, and ones. To compare, you always start with the hundreds place because it is worth the most. If the hundreds are the same, you move to the tens place. If the tens are also the same, you check the ones place.

You use three symbols to show your answer: > (greater than), < (less than), and = (equal to). Remember the hungry alligator — its mouth always opens toward the bigger number! With practice, comparing three-digit numbers will become fast and easy. You're doing a wonderful job! 🌟