NUMBER & PLACE VALUE · TEXTBOOK LESSON
Place value gives each digit its value according to its position. It underpins arithmetic, decimals, rounding, powers of ten and standard form.
Learning objectives
By the end of this lesson, you should be able to:
- Read and write numbers using place value.
- Partition numbers into place-value components.
- Compare, order and round numbers accurately.
- Use powers of ten to scale numbers.
1. Key vocabulary and definition
Definition
In a base-10 number system, moving one place left multiplies a digit's value by 10; moving one place right divides its value by 10.
digitplace valueonestenshundredspower of tenround
2. Essential facts and rules
These are the facts you should know before attempting the worked example.
Key mathematical facts
- 4,582 = 4,000 + 500 + 80 + 2.
- The first digit after the decimal point is the tenths digit.
- To round, inspect the digit immediately to the right of the required place value.
3. Standard method
A reliable method helps prevent errors and makes your reasoning easy to follow.
1
Identify the target place value.
2
Locate the digit in that position.
3
For rounding, inspect the next digit: 0-4 means keep, 5-9 means increase by 1.
4
Replace digits to the right with zeros for whole-number rounding, or remove them for decimal rounding.
5
Check that the rounded value is close to the original.
4. Worked example
Worked example
Round 47,368 to the nearest thousand.
1
The thousands digit is 7.
2
The next digit, the hundreds digit, is 3.
3
Because 3 < 5, keep the thousands digit unchanged.
4
Replace the remaining digits with zeros: 47,000.
5. Common mistakes
Watch out for these
- Starting calculations before deciding what the question is asking.
- Skipping important steps or changing notation midway through a solution.
- Accepting an answer without checking whether its size, sign or unit is sensible.
6. Video lesson
This topic is ready for a matching video lesson. The written textbook lesson is fully available now; additional videos can be added to the same lesson template.
7. Practice exercise
Complete these without looking at the answers first.
- Write 6,304 in expanded form.
- Round 8,761 to the nearest hundred.
- Which is greater: 0.507 or 0.57?
- Write 4.2 × 10³ as an ordinary number.
- Order -3, 5, -8 and 0 from least to greatest.
Show answers
- 6,000 + 300 + 4
- 8,800
- 0.57
- 4,200
- -8, -3, 0, 5
8. Chapter summary
- Understand the underlying idea before memorising a procedure.
- Use precise mathematical notation and show a logical method.
- Always check the final result.