What you need to know
Place Value
Place value is all about the value of each digit within a number. Each digit has a different value determined by its position. For example, in the number 157, the ‘7’ is just worth 7, but the ‘5’ isn’t actually worth 5 – it’s worth 50, and the ‘1’ isn’t worth 1 – it’s worth 100.
Place Value: Large Numbers
The reason they are separated into clumps of 3 digits by commas is because there is a pattern. Going from right to left, each digit is worth
One, then ten, then a hundred.
Then, after the first comma,
One thousand, then ten thousand, then a hundred thousand.
Then, the next 3 would be
One million, then ten million, and so on.
Place Value: Small Numbers
Digits after the decimal place also have a value, but this decreases the further you move away from the decimal point.
Example 1: Large Number
State the place value of the 6 in 4,609.
Counting from right to left, we can see that the 6 is in the third column along – the hundreds column. Therefore, the value of the ‘6 digit’ in this number is 600.
Note: a quick way to state how much that digit is worth is simply to make all the other digits in the number into zeros. This works the same way for decimal place value, as we are about to see.
Example 2: Small Number
In the number 0.56023, what is
a)The value of the 5?
b)The value of the 2?
a) The 5 is the first digit after the decimal place, meaning it is in the tenths column. So, it is worth
\dfrac{5}{10} \text{ or }0.5
b) The 2 is the 4th digit after the decimal place, meaning it is in the ten thousandths column. So, it is worth
\dfrac{2}{10,000}\text{ or }0.0002
In both of these cases, the trick of “making all other digits into zeros” would give us the correct answer.
Note:Questions specifically based on place value are not very common but understanding place value is super important for being able to work with numbers in all kinds of questions.
Example Questions
1) In the number 1,899, what is the value of the 8?
The 8 is the 3rd digit from the right, meaning it’s in the hundreds column. So, the value is,
800 or \text{eight hundred}
2) In the number 32.107, what is the value of the 1?
The 1 is one place after the decimal point, meaning it is in the tenths column. So, the value is,
\dfrac{1}{10} or \text{one tenth}
3) In the number 0.0461, what is the value of the 6?
The 6 is three places after the decimal point, meaning it is in the thousandths column. So, the value is
\dfrac{6}{1000} or \text{six thousdandths}
4) In the number 549,023, what is the value of the 5?
The 5 is the 6th digit from the right, meaning it’s in the hundred thousands column. So, the value is,
500,000 or \text{five hundred thousand}
5) Becky is thinking of a number. Her number has 3 thousands, 5 tens, and 1 hundredth. What is her number?
3 thousands = 3,000
5 tens = 50
1 hundredth = 0.01
Adding these all together, we get Becky’s number to be
3,000+50+0.01=3,050.01
Worksheets and Exam Questions
(NEW) Place Value Exam Style Questions - MME
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