Number & Place Value
Number and place value
Place value is the value a digit has because of its position in a number. Understanding it is the foundation of all 11+ maths.
The place value columns
Each column is ten times bigger than the one to its right:
| Thousands | Hundreds | Tens | Units | . | tenths | hundredths |
|---|---|---|---|---|---|---|
| 1000 | 100 | 10 | 1 | . | 0.1 | 0.01 |
In 3,482, the 4 means 4 hundreds (400), and the 8 means 8 tens (80).
Reading and writing large numbers
Split big numbers into groups of three with commas: 2,540,318 = two million, five hundred and forty thousand, three hundred and eighteen.
Rounding
- To the nearest 10: look at the units digit. 5 or more → round up; less than 5 → round down. 47 → 50; 43 → 40.
- To the nearest 100: look at the tens digit. 380 → 400; 340 → 300.
- The same idea works for decimal places.
Negative numbers
Numbers below zero (e.g. −3) appear on a number line to the left of 0. Useful for temperatures. Counting up from −3 by 5 gives 2 (−3 → −2 → −1 → 0 → 1 → 2).
Order of operations (BODMAS/BIDMAS)
Do calculations in this order:
1. Brackets
2. Orders (powers/indices)
3. Division and Multiplication (left to right)
4. Addition and Subtraction (left to right)
So 3 + 4 × 2 = 3 + 8 = 11 (not 14).
Worked example
What is the value of the 7 in 4,732, and round the number to the nearest hundred.
- The 7 is in the hundreds column → value 700.
- Nearest hundred: the tens digit is 3 (less than 5) → 4,700. ✓
Common mistakes
- Ignoring place value (thinking the 7 in 4,732 is just "7").
- Doing addition before multiplication — remember BODMAS.
- Rounding using the wrong digit (look at the digit to the right of the place you're rounding to).
Top tips
- Line up columns carefully when adding or subtracting.
- Say big numbers out loud in groups of three.
- Always apply BODMAS in calculations with mixed operations.
Quick recap
- Place value: each column is ×10 the one to its right; a digit's value depends on its position.
- Round using the digit to the right (5+ rounds up); negative numbers sit left of zero.
- Use BODMAS for the order of operations.