Place Value
What is place value?
- When a number is written down using digits, each digit has a value depending on where it is within the number
- For example for the number 9876
- The 6 represents 6 ones (or units)
- The 7 represents 7 tens
- The 8 represents 8 hundreds
- The 9 represents 9 thousands
- In words, this number is nine thousand, eight hundred, and seventy six
How do I read large numbers?
- Each place has a value ten times larger than the place to the right of it
- For example for the number 12345678
Ten Millions | Millions | Hundred Thousands | Ten Thousands | Thousands | Hundreds | Tens | Ones |
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
- When dealing with large numbers, it is often helpful to write them with a space between some of the digits
- We do this after every 3 digits from the right
- For example, 12345678 could be written as 12 345 678
- This number would be twelve million, three hundred and forty five thousand, six hundred and seventy eight
How does place value work for decimals?
- Each place has a value ten times larger than the place to the right of it
- This means for decimals, the decimal places further to the right are worth less
- Lets look at the number 23.45678
- We would read this as twenty three point four five six seven eight
- However, each place has a different value
Tens | Ones | Decimal Point | Tenths | Hundredths | Thousandths | Ten-thousandths | Hundred-thousandths |
2 | 3 | . | 4 | 5 | 6 | 7 | 8 |
- The 4 represents 4 tenths, or 0.4
- The 6 represents 6 thousandths, or 0.006
- You will often hear these place values used relating to time
- For example in a sprint race, athletes may be separated by "5 hundredths of a second" or 0.05 seconds
Exam Tip
- Separate large numbers into groups of three digits, from the right, to make reading them easier
- 54687321 becomes 54 687 321
- Write down the place value of each digit to help read it or identify the value of a particular digit if you need to e.g.
-
Tens Ones . Tenths Hundredths Thousandths 2 3 . 5 6 4
-
Worked example
Ten Thousands | Thousands | Hundreds | Tens | Ones |
8 | 7 | 6 | 5 | 4 |
7000
Tens | Ones | Point | Hundredths | Thousandths | Ten Thousandths |
1 | 4 | . | 2 | 6 | 3 |
3 ten thousandths of a second, or 0.003 seconds