Place Value of a Number
Let’s take a look at a couple of different numbers
1,000,000 | 100,000 | 10,000 | 1,000 | 100 | 10 | 1
These numbers seem easy enough. You have one, ten, one hundred, one thousand, ten thousand, one hundred thousand, and one million. If you look closely you can see that if you multiply each number by 10 you get the number to the left. So, 1X10 is 10, 10X10 is 100, 100X10 is 1,000, and so on. In any number, the same is true. The digit to the left has a place value that is 10 times the place to it’s right.
Let’s try adding all these together, and see what number we get.
1,000,000 + 100,000 + 10,000 + 1,000 + 100 + 10 +1 += 1,111,111
You get one million one hundred eleven thousand one hundred eleven. We can see how the place value increases by 10x as you move to the left.
Let’s try another:
Find the place value of 8 in 9,865.
Now if we rewrite this we can make this a little easier to visualize.
9,000 + 800 + 60 +5
So this is 9 thousands + 8 hundreds + 6 tens +5 ones.
So let’s look back at our problem. Find the place value of the 8 in 9,865. So, we are looking for the place value of this 8 right here. When we write it out we can clearly see that 8 is in the hundreds place.
Now, try one on your own.
In the following numbers the digit 6 represents a value of 1,000 in which number.
Let’s start with “a.” I’m going to expand it so we can see it more clearly.
60,000 + 7,000 + 400 + 10 + 9
6 ten thousands + 7 thousands + 4 hundreds + 1 ten + 9 ones
Now, we are able to see that in choice “a” there is a 7 in the thousands place.
So, let’s move on to choice “b. 236,798.”
As you get more, and more familiar with finding place values it will become second nature; but for now we will continue to expand our numbers.
So we have:
200,000 + 30,000 + 6,000 +700 + 90 + 8
2 hundred thousands + 3 ten thousands + 6 thousands + 7 hundreds + 9 tens + 8 ones
Now, let’s look back and see what our problem was asking for “The digit 6 in which number represents a value of 1,000.”
Well, we can see that we have a 6 in the thousands place. So, “b” is our answer! Great work guys.
If rewriting and expanding the number is not a helpful method for you, then let’s try one more thing.
When you have a whole number, and there are no digits to the right you know that you are dealing with a number in the ones place; like 7.
When there is one other digit to the right, then you are in the tens place; like 70.
When there are two digits to the right, then you are in the hundreds place; like 700.
If there are 3 digits to the right, then you are in the thousands place; like 7,000.
If there are 4, you are in the ten thousands place; like 70,000.
If there are 5, you are in the hundred thousands place.
If there are 6, you are in the millions place, and so on.
Practice finding place values on your own by making up your own whole numbers, and writing out the place value for each of the digits.
So far, we have only looked at whole numbers; so, let’s take a look at decimal numbers.
Remember, every digit to the left of the decimal is a whole number, and every digit to the right is a fraction or decimal number. Since, we already know how to identify place values for whole numbers, for now, let’s just look at everything to the right of the decimal.
So, we have our decimal point ‘.’ then 521.
Let’s simplify, we have:
5/10 + 2/100 + 1/1,000
5 tenths + 2 hundredths + 1 Thousandths
The digit to the very right of the decimal represents the tenth place value.
The digit second digit to the right of the decimal represents the hundredths place value, and so on.
One important thing to note is that there is not a oneth place. There is only a ones place, because 1/1 is equal to 1, and 1 is a whole number.
I hope this video helped you to better understand number place values. Be sure to practice on your own until you feel confident in your ability to correctly identify place values.
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