What you need to know
Each digit in a number is worth a different amount depending on whereabouts in the number it is. 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. This is known as place value, and to see it in action, observe that we can write
A bigger example:
In this number, you can see that the value on the far right starts with just “ones”, i.e. the amount the digit is worth is the digit itself, and then, going from right to left, each column is worth ten times as much as the last. For example, the 3 is worth 30, since it’s in the tens column, but the 2 is worth 2,000, as it’s in the thousands column.
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, still going from right to left, each digit is worth
One thousand, then ten thousand, then a hundred thousand.
You can see that it’s the same as the previous 3, except they’ve all had “thousand” stuck on the end. Exactly the same thing will happen every time we move up by 3 digits, but this time it’s important to understand that
a thousand thousand = a million.
Then, the next 3 will be
One million, then ten million, then a hundred million.
Example: 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.
Decimal Place Value
Once you understand place value for integers, extending the idea to decimals is not too tricky.
As seen in the picture above, the first digit after the decimal point is in the “tenths” column, and it is worth 0.4 or 4/10. Then, as you move alone, from left to right this time, each digit is ten times smaller than the last.
However, they still follow the same pattern, just in the other direction! And this time, the name of each place ends with “ths”. In other words, the place values after the decimal point are
A tenth, a hundredth, one thousandth, ten thousandth, a hundred thousandth, and so on…
Example: 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 }0.5b) 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 }0.0002In both of these cases, the trick of “making all other digits into zeros” would give us the correct answer.
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 contexts.
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 of it is 800.
2) In the number 32.107, what is the value of the 1?
The 1 is one space after the decimal point, meaning it is in the tenths column. So, the value of it is 0.1 (or 1/10).
3) 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=3,005.01
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