What is Place Value in Maths?
Place value provides us with an understanding of the individual digits within a number, based on their position or place value.
Although we write and read numbers from left to right, we move from right to left when considering the place value of the individual digits within a number.
How to Determine the Individual Value of Digits in a number
In order to demonstrate this, I will use the number 158 as an example.
| Hundreds | Tens | Ones |
| 1 | 5 | 8 |
- The value of the 8 within 158 is = 8 ones or 8 x 1 = 8
- The value of the 5 within 158 is 5 tens or 5 x 10 = 50
- The value of the 1 within 158 is 1 hundred or 1 x 100 = 100
The first block of three columns on the place value grid is called the ‘units’ block. Following on from the units block, we have another block of three columns which is called the 'thousands' block.
Just like the units block, the columns within the thousands block are one, ten and hundred. In this case however, each column has a value of thousand and therefore, the value of the columns will be one thousand, ten thousand and hundred thousand.
Lastly, we will consider the the millions block which lies to the left of the thousands block. Once again, we have a column for one, ten and a hundred, though the value of these columns differs to the previous ones we have looked at. Indeed this time we have one million, ten million and a hundred million.
To summarise the above, the columns one, ten and hundred repeat indefinitely on the place value grid. As I have shown to you though, each block of one, ten and hundred has a different label.
Labelling the Columns on a place value grid
We can use either words or numerical values to label the columns in a place value grid. Given below is an example of both types of labels on a place value grid.
| Thousands (000s) | Units (1s) | ||||
| Hundreds 100 | Tens 10 | Ones 1 | Hundreds 100 | Tens 10 | Ones 1 |
| 2 | 4 | 3 | 1 | 5 | 8 |
As I said previously, we group the place value grid in to blocks of three columns. There are two main reasons for doing this which, I shall discuss below:
- It makes it easier to determine where to put the commas in a number
Commas are placed at the end of each block, moving from left to right (the same direction in which we read a number).
Using the example above, we would place a comma between the 3 (one thousands column) and 1 (hundreds column).
243,158
2. It also makes it easier to read numbers and write them in words
How to read and write numbers using the place value grid
Once again, I will use the place value grid and number from above to demonstrate how to read and write numbers using the place value grid.
To read or write a number, we must start from the left, moving to the right. While doing this, we must consider each individual block of three columns, one at a time.
The first block within the number 243,158
So, the first block of three in the number 243,158 is the ‘thousands’ block.
In any given block, we read the digits collectively, just as we would read a regular three, two or one digit number. In this case, we have 'Two Hundred and Forty Three'.
Once we have our number, we then add on the block name at the end of it. As has been noted, this number belongs to the ‘Thousands' block and so, we have two hundred and forty thousand to begin with.
The Next Block in the number 243,158
The method I have outlined above, works for every block however, it does not work for the 'units' block. The only difference with the units block is that we do not add the block name at the end - besides that, the method remains the same.
Referring back to the number we have been working with above, we can see there is one hundred and fifty-eight in the units block. This will now be written in front of the two hundred and forty three thousand that we previously wrote down.
The last step , when writing out the entire number is that we must place a comma to separate each block, starting from left to right. This is identical to what we do when writing the number out in numerical form. It is however important to note that we do not write the word ‘and’ between blocks.
Finally, the number we have is:
Two Hundred and Forty Thousand, One Hundred and Fifty-Eight (not Two Hundred and Forty Thousand and One Hundred and Fifty-Eight)
Key Words for Place Value in Maths
To finish off, I would like to share a list a list of vocabulary that is commonly used within the topic of place value.
- Number – A numerical representation of a quantity. Numbers are made up of one or more digits
- Digits - The individual numerical values which are part of a number that is made up of more than one digit. E.g. 25 is a number made up of the digits 2 and 5
- Column - Refers to the vertical division on a place value grid
- Block - Collection of three columns with a unique label or name such as 'Millions'
- Place Value - The name of the column a specific digit sits in on a place value grid
- Value - The worth of an individual digit within a number e.g. 5 in the tens column has a value of 5 tens = 5 x 10 = 50
- Partitioning – Using place value to split a number into its individual digits and their value. E.g. 137 partitioned would be 100, 30 and 7.
- Times larger - Each subsequent column on the place value grid is ten times larger than the previous (note: we are moving from right to left). This means that the value of each subsequent column is equal to the value of the previous one 'times' which means multiplied, by ten.
- Ascending – arranged from smallest to largest
- Descending – arranged from largest to smallest
Place Value Homeschooling Resources
I hope you are feeling more confident about place value after reading this post. In case you would like resources for your children, or just to test your own knowledge and skills, I have a bundle of place value resources on Etsy
If you would like to see more main lesson book pictures (like the one above), please visit my photo library .
I would like to thank you for reading/sharing/commenting and supporting my work. If you have any questions about this post, please comment on the post and I shall respond to your query.
