Comparing and Ordering Three-Digit Numbers

When we look at numbers up to $1,000$, we often need to figure out which number is bigger, which is smaller, or if they are exactly the same. We do this by looking at the place value of their digits.

The Comparing Symbols

We use three special math symbols to compare numbers:

• Greater than ($>$): The open side faces the bigger number. (Example: $5 > 3$)
• Less than ($<$): The pointy side points to the smaller number. (Example: $2 < 4$)
• Equal to ($=$): The numbers are exactly the same. (Example: $7 = 7$)

Tip: Think of the $>$ and $<$ signs as a hungry alligator's mouth. The alligator always wants to eat the bigger number!

How to Compare Three-Digit Numbers

To compare numbers like $345$ and $354$, we check the digits from left to right: Hundreds, Tens, then Ones.

1. Compare the Hundreds: Look at the first digit. The number with the bigger hundreds digit is greater.
   • Example: $412 > 299$ because $4$ hundreds is more than $2$ hundreds.
2. Compare the Tens: If the hundreds are the same, look at the middle digit.
   • Example: Which is greater, $789$ or $798$? Both have $7$ hundreds. Next, look at the tens: $8$ tens is less than $9$ tens. So, $798 > 789$.
3. Compare the Ones: If both the hundreds and tens are the same, look at the last digit.
   • Example: Compare $345$ and $348$. Both have $3$ hundreds and $4$ tens. Since $5 < 8$, we know that $345 < 348$.

Ordering Numbers

Once you know how to compare two numbers, you can order a whole group of them! You can put them in order from least to greatest (smallest to biggest) or greatest to least (biggest to smallest).

Example: Order $521$, $512$, and $251$ from least to greatest.

1. Find the smallest number first. Look at the hundreds: $5$, $5$, and $2$. The number $251$ has the smallest hundreds digit, so it goes first.
2. Now compare the remaining numbers: $521$ and $512$. Both have $5$ hundreds. Look at the tens: $1$ ten is less than $2$ tens, so $512$ is smaller than $521$.
3. Put them in order: $251, 512, 521$.