Model Whole Numbers
Our number system is called a place value system because the value of a digit depends on its position, or place, in a number. The number 537 has a different value than the number 735. Even though they use the same digits, their value is different because of the different ...
Model Whole Numbers
Our number system is called a place value system because the value of a digit depends on its position, or place, in a number. The number \(537\) has a different value than the number \(735\). Even though they use the same digits, their value is different because of the different placement of the \(3\) and the \(7\) and the \(5\).
Money gives us a familiar model of place value. Suppose a wallet contains three \($100\) bills, seven \($10\) bills, and four \($1\) bills. The amounts are summarized in the figure below. How much money is in the wallet?
Image credit: OpenStax Prealgebra
Find the total value of each kind of bill, and then add to find the total. The wallet contains \($374\).
Base-10 blocks provide another way to model place value, as shown in the figure below. The blocks can be used to represent hundreds, tens, and ones. Notice that the tens rod is made up of \(10\) ones, and the hundreds square is made of \(10\) tens, or \(100\) ones.
Image credit: OpenStax Prealgebra
The figure below shows the number \(138\) modeled with \(\text{base}\)-\(10\) blocks.
We use place value notation to show the value of the number \(138\). Image credit: OpenStax Prealgebra
| Digit | Place value | Number | Value | Total value |
|---|---|---|---|---|
| \(1\) | hundreds | \(1\) | \(100\) | \(100\) |
| \(3\) | tens | \(3\) | \(10\) | \(30\) |
| \(8\) | ones | \(8\) | \(1\) | \(8\) |
| \(\text{Sum} = 138\) |
Example
Use place value notation to find the value of the number modeled by the \(\text{base}\)-\(10\) blocks shown.
Image credit: OpenStax Prealgebra
Solution
There are \(2\) hundreds squares, which is \(200.\)
There is \(1\) tens rod, which is \(10.\)
There are \(5\) ones blocks, which is \(5.\)
| Digit | Place value | Number | Value | Total value |
|---|---|---|---|---|
| \(2\) | hundreds | \(2\) | \(100\) | \(200\) |
| \(1\) | tens | \(1\) | \(10\) | \(10\) |
| \(5\) | ones | \(5\) | \(1\) | \(5\) |
| \(\text{Sum} = 215\) |
The \(\text{base}\)-\(10\) blocks model the number \(215.\)
Video: Writing a Whole Number in Digits from Words
We'll talk more about this in the next lesson. Video credit: Mathispower4u
This lesson is part of:
Introducing Numbers