Comparing and Ordering Multi-Digit Numbers

When dealing with large numbers, you often need to figure out which number is larger or arrange them in a specific order. To do this, we use place value and three important math symbols:

• $<$ means less than
• $>$ means greater than
• $=$ means equal to

How to Compare Multi-Digit Numbers

To compare two numbers, follow these simple steps:

1. Line up the numbers by their place values. If one number has more digits than the other, the number with more digits is always greater.
2. Start at the highest place value (the digit farthest to the left).
3. Compare the digits. If they are the same, move one place to the right until you find digits that are different.

Example: Compare $45{,}678$ and $45{,}768$

Let's look at the digits from left to right:

• Ten Thousands: Both numbers have a $4$.
• Thousands: Both numbers have a $5$.
• Hundreds: The first number has a $6$, and the second number has a $7$.

Since $6 < 7$, the entire first number is smaller. $45{,}678 < 45{,}768$

Ordering Multi-Digit Numbers

Ordering numbers just means comparing three or more numbers and putting them in a sequence, usually from least to greatest or greatest to least.

Example: Order $304{,}200$; $340{,}200$; and $304{,}020$ from least to greatest.

1. Look at the highest place value (Hundred Thousands): All three numbers start with a $3$.
2. Look at the Ten Thousands place:
   • $304{,}200$ has a $0$
   • $340{,}200$ has a $4$
   • $304{,}020$ has a $0$ Because $4$ is the largest, $340{,}200$ is the greatest number.
3. Compare the remaining two numbers: $304{,}200$ and $304{,}020$.
   • Thousands place: Both have a $4$.
   • Hundreds place: $304{,}200$ has a $2$, and $304{,}020$ has a $0$.
   • Since $0 < 2$, $304{,}020$ is the smallest.

Final Order (Least to Greatest): $304{,}020 < 304{,}200 < 340{,}200$