A place value house consists of rooms with hundreds, tens and ones. The prerequisite for a place value house is that each room will comprise only one digit, ranging from 0 to 9. Any number can be written in a place value house.
To make it more clear, let’s represent the number 67 in the place value house.
Here, the value of 6 and 7 is:
In math, every digit in a number has a place value.
Place value can be defined as the value represented by a digit in a number based on its position in that number.
Here’s an example that demonstrates the relationship between the place or position and the place value of the digits in a number:
The number 430 is represented as:
Here, 3 represents 3 tens, or 30.
However, the 3 in the number 375 represents 3 hundreds, or 300.
It is important to understand that a digit can be the same but its value depends on where it is placed in a number.
Dienes blocks are cubes that are used to represent units or ones, tens, hundreds, and thousands.
For example, the number 258 can be represented by Dienes blocks as shown below:
However, if we have another number, like 300, it is represented as:
Since we have 0 in the place of tens and ones, it is not represented by any of the Dienes blocks.
As you can observe, the concept of place value is easier to understand if the number is represented by Dienes blocks.
For example: Write down the number of tens. Write down the number of hundreds. Then write the number.
Count the number of tens Dienes
Total tens Dienes = 47
Example 1: Find the number.
We have 5 hundreds Dienes, 4 tens Dienes, and 9 ones Dienes.
Accordingly, we fill the place value house:
Then we fill in the blanks
Example 2: Find the value of the underlined digit 796.
The value of the underlined digit is 90.
Example 3 : A class has 40 boxes of pencils. Each box has 10 pencils. The class needs 800 pencils. How many more boxes does the class need?
A class has 40 boxes of pencils, and each box has ten pencils.
In other words, we have 40 tens.
\( = 40\times 10 \)
\( = 400 \) pencils.
Therefore, the class has 400 pencils.
But the class needs 800 pencils.
Therefore, the remaining number of pencils we need is 800 – 400 = 400 pencils.
Example 4 : There are 674 fruit trees planted in a park. 500 are apple trees, 104 orange trees, and the rest are cherry trees. How many cherry trees have been planted?
There are 70 cherry trees that have been planted in the park.
Understanding place value is important because it will help us in comprehending numbers and the values of the digits in a number.