01Why this matters
A price of $204 is very different from $240. Reading the positions of digits helps you check prices, measurements and large numbers without relying on guesswork.
02See it
03Understand it
Place value is the value a digit has because of its position in a number.
Our number system groups things in tens. Ten ones make one ten; ten tens make one hundred. Moving one column to the left multiplies the value of a digit by ten. A zero holds an empty place: in 305, there are three hundreds, no tens and five ones. To the right of the decimal point, the places are tenths, hundredths and thousandths.
04Guided example
What is the value of the 7 in 4,728?
- Read from the right: 8 is in the ones column and 2 is in the tens column.
- The 7 is in the hundreds column, so it represents 7 × 100 = 700.
- Check by expanding the whole number: 4,000 + 700 + 20 + 8 = 4,728.
05Try it
06Practise it
07Use it in the real world
A meter reading of 12,406 litres contains 400 litres in its hundreds place. Keeping the zero in the tens column prevents recording 12,460 by mistake.
Go a little deeper
Base ten is a convention, not a law of nature. Computers often use base two. In any positional system, each place is a power of the base.
08Quick check
09Summary
Place value is the value a digit has because of its position in a number. Check by expanding the whole number: 4,000 + 700 + 20 + 8 = 4,728.
Before moving on, explain the worked example in your own words. Use the hint on any question you want to revisit.
10Key idea
4,728 = 4 × 1,000 + 7 × 100 + 2 × 10 + 8
Each digit is multiplied by its place value. No physical units are required.
10 ones = 1 ten; 10 tens = 1 hundred
Find this in the formula library →