Place Value
If you counted the digits we use in mathematics, you would see that we only use 10 digits (0 - 9) for all the numbers we express in mathematics.
So, if our number system is based off of 10 digits how do we express higher and higher numbers in an orderly way? Well, we give each place a value, when we write a number.
When we write a number, we start off with the number to the right and give it a value of one. We can have 4 ones, 3, ones, 2 ones, 9 ones, etc., but when we get to 10, we put a 0 in the ones place and a 1 in the tens place directly to the left. Instead of just saying we have 10 ones, we say we have 1 ten.
Now we can have as many tens as we want….from 0 tens to 9 tens, but when we get to 10 tens, we put a 0 in the tens place and put a 1 in the hundreds place. We could say we have 10 tens, but we just say we have 1 hundred.
We can have as many hundreds as we want from 0 - 9, but when we get to 10 hundreds, we say we have 1 thousand, instead of 10 hundreds.
So, you get the picture, this goes on forever and every—literally.
So, 1 = 1
(1 x 1) = 1
10 ones = 10, (1 x 10) = 10
10 tens = 100, (10 x 10) = 100
10 hundreds = 1,000, (100 x 10) = 1,000
In the number 1,000, we have 1,000 ones, or you could state it as 100 tens, or you could state it as 10 hundreds or simply as 1 thousand.
In the number above, we have 7 ones, 5 tens, and 1 hundred….that equals the number 157.
Expanded Form
You may be asked to write number like this in expanded form. The expanded form of this number is:
100 + 50 + 7
You can see in the number 111, that the place value to the left is 10 times greater than the place value to the right (i.e., 1 x 10 = 10, 10 x 10 = 100).
So as we go from right to left, we can express larger and larger numbers.
If fact, if you dealt with the cost of business products around the world you would have to count into the trillions. Each time we move to the left, it’s like we are multiplying the place value, from which we are moving, by 10.
So, we get to express larger and larger numbers, simply, without having to write the number one, over and over again….200,000 times!
Summary
Each place in a number has a value.
As you move from left to right you go up—the place value to the left is 10 times greater than the place value to the right.
Expanded form separates out each place value in this way 546 = 500 + 40 + 6.
Become familiar with larger numbers because they become important in business, real estate, science, politics and more.