Converting Between Place Values Up to 999

Every number up to 999 can be broken into hundreds, tens, and ones. Converting between place values means changing how a number is grouped without changing its value. For example, 3 tens can be renamed as 30 ones, and 130 ones can be renamed as 1 hundred, 3 tens. This skill is closely tied to identifying hundreds, tens, and ones, since you need to know what each digit represents before you can trade it for another place value.

Place value works in groups of ten. That gives one simple rule to remember:

\( 10 \) ones \( = 1 \) ten, and \( 10 \) tens \( = 1 \) hundred.

This means you can always trade 10 units in one place for 1 unit in the next place up, or trade 1 unit for 10 units in the place below it. Nothing about the number changes, only how it is grouped.

Suppose you have 47 tens and want to know what number that makes. Since 10 tens make 1 hundred, divide 47 by 10 to see how many whole hundreds you can trade for.

\( 47 \div 10 = 4 \) remainder \( 7 \), so 47 tens becomes 4 hundreds and 7 tens, which is the number 470.

Here is a second example using ones. If you have 235 ones, how many hundreds, tens, and ones is that?

\( 235 \div 100 = 2 \) hundreds, with 35 left. \( 35 \div 10 = 3 \) tens, with 5 ones left. So 235 ones regroups into 2 hundreds, 3 tens, and 5 ones, which is 235.

You can also go the other way and break a bigger place value into smaller pieces. Take the number 4 hundreds, 3 tens, 6 ones. If you break every hundred into tens, then 4 hundreds becomes \( 4 \times 10 = 40 \) tens. Add the 3 tens already there, and you get 43 tens, plus the 6 ones stay the same.

If instead you break everything down into ones, 4 hundreds becomes \( 4 \times 100 = 400 \) ones, 3 tens becomes \( 3 \times 10 = 30 \) ones, and the 6 ones stay as 6 ones. Add them together: \( 400 + 30 + 6 = 436 \) ones total.

Converting between place values is really the same skill as regrouping, and it is what makes addition, subtraction, and later operations with three-digit numbers possible. If you already understand place value models up to 999 and can write numbers using expanded form, converting between hundreds, tens, and ones is just one more way of showing the same number in a different, useful shape. Once a number is broken apart or combined, always add the pieces back together to make sure the total matches the number you started with.

Convert 6 hundreds, 12 tens, 4 ones into a number using only hundreds, tens, and ones digits.

Since 12 tens is more than 10 tens, trade 10 of those tens for 1 more hundred: \( 12 - 10 = 2 \) tens remain, and the hundreds become \( 6 + 1 = 7 \). The result is 7 hundreds, 2 tens, 4 ones, which is the number 724.

Practicing this kind of conversion alongside regrouping place values up to 999 will make three-digit addition and subtraction feel much more natural.

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• Math 2