What is place value?
Every year builds place value: four-digit numbers in Year 4, up to 1,000,000 in Year 5 and 10,000,000 in Year 6. Below: what it means, a worked example, the mistake to watch for and an 11+ question.
The answer
Place value is the value a digit has because of where it sits in a number.
What it means
In 4,372 the 3 is worth 300, because it is in the hundreds column. The 7 is worth 70 and the 2 is worth 2.
Each column is worth 10 times the column to its right: ones, tens, hundreds, thousands and so on. After the decimal point come tenths and hundredths.
Zero is a placeholder. In 205 the 0 shows there are no tens, and keeps the 2 in the hundreds column.
A worked example
What happens to the digits of 47 when you multiply or divide by 10 and 100?
- 47 × 10 = 470: the 4 moves from the tens to the hundreds, the 7 from the ones to the tens, and a 0 holds the ones column.
- 47 × 100 = 4,700: every digit moves two columns to the left.
- 47 ÷ 10 = 4.7: the 4 moves to the ones and the 7 to the tenths.
- 47 ÷ 100 = 0.47: every digit moves two columns to the right, so 4 tenths and 7 hundredths.
The common mistake
Giving the digit instead of its value. In 3,512 the digit 5 is worth 500, not 5.
How it comes up in the 11+
What is the value of the 8 in 3,086,425?
Answer: 80,000
- Read the columns from the left: 3 millions, 0 hundred thousands, 8 ten thousands.
- So the 8 is worth 8 ten thousands, which is 80,000.
Try it yourself
The chart opens on 47 from the worked example. Multiply or divide by 10 or 100 and watch every digit move while the decimal point stays still.
On a place value chart, multiplying by 10 moves every digit one column to the left.
Related words and practice
More maths words
Questions parents ask
What is a placeholder?
A zero that fills an empty column so the other digits stay in the right place. Without it, 205 would become 25.
What happens to the digits when you multiply by 10?
Every digit moves one column to the left, so it is worth 10 times as much. The decimal point stays still: 3.6 × 10 = 36.
Knowing the words is half of an 11+ maths question
11+ papers use maths vocabulary without explaining it. The free diagnostic checks maths, English and both kinds of reasoning, and shows what to practise next. No card is required.