Numbers are built with digits, just like words are built with letters. The cool part is that a digit's value changes depending on its position, or place, in a number. This idea is called place value.

Let's look at the number 347. It has three digits: 3, 4, and 7. Each one sits in a different spot and holds a different value.

• The 7 is in the ones place. Its value is just 7.
• The 4 is in the tens place. Its value is 4 tens, or 40.
• The 3 is in the hundreds place. Its value is 3 hundreds, or 300.

So, the number 347 is really just a shorthand way of writing $300 + 40 + 7$. Every three-digit number works this way. The position on the right is for ones, the middle is for tens, and the left is for hundreds.

This pattern continues as numbers get bigger. After the hundreds place comes the thousands place, then ten thousands, and so on. Understanding this system is the key to working with any number, no matter how large.

Now let's look at a simple way to sort numbers into two groups: even and odd.

An even number is any number that can be divided by 2 with nothing left over. Think of pairing things up. If you have 6 cookies, you can give 2 to a friend, 2 to another, and keep 2 for yourself. Everyone gets the same amount, with none left. So, 6 is an even number.

An odd number is any number that has a remainder of 1 when divided by 2. If you have 7 cookies and try to share them between two people, one person will always get an extra cookie. There's an odd one out. So, 7 is an odd number.

This trick works for any number, no matter how big. The number 58 is even because its last digit is 8. The number 921 is odd because its last digit is 1.

Once you understand place value, you can easily compare numbers to see which is bigger. We use special symbols for this: > means "greater than," < means "less than," and = means "equal to."

To compare two numbers, start with the largest place value. Let's compare 452 and 437.

1. Check the hundreds place. Both numbers have a 4 in the hundreds place. So far, they're tied.
2. Move to the tens place. The first number has a 5 (value 50), and the second has a 3 (value 30). Since 5 is greater than 3, we know that 452 is greater than 437.

We don't even need to look at the ones place. We can write our comparison as $452 > 437$.

Ordering a group of numbers works the same way. Just compare them two at a time to put them in order from least to greatest or greatest to least. For example, to order the numbers 192, 98, and 201 from least to greatest, you'd find the smallest first (98), then the next smallest (192), and then the largest (201). The final order is 98, 192, 201.

Time to check your understanding.

Great work. Building a strong sense of how numbers work is the first step toward mastering math.