Comparing and Ordering Large Numbers

When working with numbers up to 10,000, it is important to know how to figure out which number is bigger, which is smaller, or if they are exactly the same. We do this by comparing their place values!

The Comparing Symbols

We use three special math symbols to compare numbers:

• $>$ (Greater Than): The open side always points to the bigger number. (Example: $5 > 3$)
• $<$ (Less Than): The pointy end points to the smaller number. (Example: $2 < 8$)
• $=$ (Equal To): Both numbers have the exact same value. (Example: $4 = 4$)

How to Compare Large Numbers

To compare two large numbers, always start by looking at the highest place value (the digit farthest to the left).

Let's compare $4{,}567$ and $4{,}576$:

1. Thousands Place: Both numbers have a $4$. Since $4 = 4$, move to the next digit.
2. Hundreds Place: Both numbers have a $5$. Since $5 = 5$, move to the next digit.
3. Tens Place: The first number has a $6$, and the second number has a $7$.

Since $6$ is less than $7$, the entire first number is smaller.

$4{,}567 < 4{,}576$

Ordering Large Numbers

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

Let's order these numbers from least to greatest: $8{,}432$, $8{,}342$, and $8{,}234$.

1. Look at the thousands place: They all start with an $8$.
2. Look at the hundreds place: The digits are $4$, $3$, and $2$.
3. Compare the hundreds: $2$ is the smallest, $3$ is in the middle, and $4$ is the biggest.

So, the correct order from least to greatest is:

$8{,}234 < 8{,}342 < 8{,}432$