When we write numbers out the position, or place value, of each number tells us something important. So if we have the number 57 we can think of 5 being in the ‘tens’ column and 7 being in the ‘units’ column shown in (a) below:
a) Five tens or 5 x 10 or 50
Seven units or 7 x 1 or 7
(b) Likewise, for the number 831:
Eight hundreds or 8 x 100 or 800
Three tens or 3 x 10 or 30
One unit or 1 x 1 or 1
You can summarise the Hundreds, Tens and Units by using the letters H, T and U above each column. You can write these above your numbers any time you’re trying to work out the place values.
As you can see from the diagram to the right, we can also have bigger numbers:
Thousands = Th
Tens of Thousands = TTh
Hundreds of Thousands = HTh
And so on…
Knowing what each individual digit in a number represents can help you with adding, subtracting and other operations. For many people this knowledge forms the foundation of other things they will learn in maths, but everyone can benefit from going over it to make sure it’s well understood.
Relationship between the places
Notice that each time we move one place to the left, say from tens to hundreds, the value of that place is 10 times bigger. So a hundred is ten times bigger than ten. And ten, is ten times bigger than one.
We can also go the other way and reverse the operation.
In this case we’re dividing by ten each time.
Have a go at the following to check you’ve understood.
Q1 – How many hundreds are there in 4,635?
A1 – 6 hundreds
Q2 – How many units are there in 942?
A2 – 2 units
Q3 – How many thousands are there in 7,890?
A3 – 7 thousands
Q4 – How many tens are there in 105?
A4 – None. (there is one hundred and five units though)
In the next post, Place Value: Decimals, we’ll show that you that you can apply this logic to places beyond the decimal point and into the world of less-than-one. Then you might want to move onto Multiplying and Dividing by Ten. In the mean time let me know how you got on with place value in the comments below. If you have a suggestion for a topic to cover, email me at firstname.lastname@example.org.