The number system
Understanding place value
The value of a digit depends on its position in the number. The same digit can be worth different amounts in different places.
How place value works
Each place is worth ten times the place to its right. After the decimal point come the tenths and then the hundredths. Example: in 12345.67 the digit 3 is in the hundreds place, so it is worth 300.
Decomposing a number
You can break a number into the value of each digit. For example, 649 = 600 + 40 + 9.
Worked examples
Value of a whole-number digit
- Look at 6703.46 and find the digit 7.
- The 7 is in the hundreds place.
Answer: The value of the 7 is 700.
Value of a decimal digit
- Look at 70213.8 and find the digit 8.
- The 8 is just after the decimal point, in the tenths place.
Answer: The value of the 8 is 0.8.
Decomposing a number
- Take the number 649.
- Split it into hundreds, tens and ones.
Answer: 649 = 600 + 40 + 9
Where you see this in real life
- Knowing that $300 is much more than $30 when you go shopping.
- A doctor giving 10 ml of medicine — ten times more than 1 ml.
- Reading large numbers on prices and populations.
Key words
- Digit
- One of the symbols 0–9 used to write numbers.
- Place value
- The value of a digit because of its position in the number.
- Tenth
- The first place after the decimal point — one part out of ten.
- Hundredth
- The second place after the decimal point — one part out of a hundred.