11+ Maths · Topic explained
Place value
Why is the 7 in 700 worth so much more than a plain 7?
The big idea
Where a digit sits decides what it's worth: each place is ten times the place on its right.
Picture it
Each column is like a bigger coin: the further left, the more every digit there is worth.
Key words
- digit
- One of the ten symbols 0 to 9 that we build numbers from.
- place value
- What a digit is worth because of the column it is in.
- decimal point
- The dot between the ones and the tenths.
- placeholder
- A zero that keeps the other digits in their right places, as in 507.
Worked examples
- 1Warm-up
What is the 6 worth in 4,682?
- The 6 is in the hundreds column
- So it is worth 600
- 211+ standard
What is the 3 worth in 25.437?
- After the point: tenths, hundredths, thousandths
- The 3 is in the hundredths column
- It is worth 3 hundredths = 0.03
- 311+ standard
Work out 3.07 × 100
- × 100 moves every digit two places to the left
- 3.07 × 100 = 307
- 411+ standard
Write in figures: five million, forty thousand and six
- 5 millions, 0 hundred thousands, 4 ten thousands
- 0 thousands, 0 hundreds, 0 tens, 6 ones
- Zeros hold the empty places: 5,040,006
The common mistake
The mistake
0.45 is bigger than 0.5, because 45 is bigger than 5.
Instead
0.5 is bigger: it is 0.50, and 5 tenths beats 4 tenths.
Why: Compare decimals column by column from the left, not by how many digits they have.
Where it comes up in the 11+
Digit values, ordering decimals, × and ÷ by 10, 100 and 1,000, and writing big numbers in words or figures.
The video
Video coming soon
We're making a short video that explains place value step by step. Until then, everything it covers is on this page.
Free printable
Place value worksheet
Practice questions on this topic to print and try on paper, at home or on the way to school.
Download the worksheet (PDF)Free account needed: it takes a minute.
Quick quiz
Have a go first, then tap to see the answer.
1. What is the 9 worth in 59,214?
- 9
- 90
- 900
- 9,000
- 90,000
Show the answerHide the answer
9,000
The 9 is in the thousands column.
2. Which is the largest: 0.7, 0.65, 0.07 or 0.699?
- 0.7
- 0.65
- 0.07
- 0.699
Show the answerHide the answer
0.7
0.7 = 0.700: it has the most tenths (7).
3. What is 42.5 ÷ 100?
- 4.25
- 0.425
- 0.0425
- 425
Show the answerHide the answer
0.425
÷ 100 moves every digit two places to the right.