NUMBER · TEXTBOOK LESSON
Decimals are another way to represent fractions with denominators based on powers of ten. Place value continues to the right of the decimal point through tenths, hundredths, thousandths and beyond.
Learning objectives
By the end of this lesson, you should be able to:
- Read and write decimal numbers accurately.
- Relate decimals to fractions and percentages.
- Compare and order decimals using place value.
- Calculate with decimals while maintaining correct place-value alignment.
1. Key vocabulary and definition
Definition
0.4 means four tenths, so 0.4 = 4/10. 0.04 means four hundredths, so 0.04 = 4/100.
decimal pointtenthshundredthsthousandthsplace value
2. Essential facts and rules
These are the facts you should know before attempting the worked example.
Key mathematical facts
- Trailing zeros after a decimal do not change value: 0.5 = 0.50.
- When adding or subtracting decimals, align decimal points.
- Multiplying by 10, 100 or 1000 changes place value; do not think of the decimal point as physically moving.
3. Standard method
A reliable method helps prevent errors and makes your reasoning easy to follow.
1
Write numbers with decimal points vertically aligned.
2
Add placeholder zeros if they make place values clearer.
3
Calculate as with whole numbers.
4
Place the decimal point in the answer directly below the decimal points above.
5
Estimate to check the result.
4. Worked example
Worked example
Calculate 4.75 + 2.8.
1
Write 2.8 as 2.80 so the place values line up.
2
Hundredths: 5 + 0 = 5.
3
Tenths: 7 + 8 = 15 tenths; write 5 tenths and regroup 1 whole.
4
Ones: 4 + 2 + 1 = 7. Therefore 4.75 + 2.80 = 7.55.
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 0.37 as a fraction over 100.
- Which is greater: 0.6 or 0.56?
- Calculate 3.48 + 1.7.
- Calculate 8.2 - 3.65.
- Round 5.784 to two decimal places.
Show answers
- 37/100
- 0.6
- 5.18
- 4.55
- 5.78
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.