Decimals Notes, Quizzes & Revision
๐ Revision Notes โข ๐ Quizzes โข ๐ Past Papers available in app
Mathematics โ Numbers: Decimals
Age: 11 (Kenyan upper primary)
Learning objectives
- Understand place value in decimals (tenths, hundredths, thousandths).
- Change between simple fractions and decimals (tenths and hundredths).
- Add, subtract, multiply and divide decimals by powers of 10 and by each other (simple examples).
- Round decimals and compare/order decimals.
- Use decimals in money and measurement contexts.
1. What is a decimal?
A decimal is a way to write numbers that are not whole. We use a dot called the decimal point to separate whole numbers from parts:
3.4 (three point four) = 3 + 4 tenths (4/10).
2. Place value for decimals
Each place to the right of the decimal point has a name and value:
| Hundreds | Tens | Ones | Decimal point | Tenths (1/10) | Hundredths (1/100) | Thousandths (1/1000) |
| 0 | 2 | 5 | . | 3 | 7 | 0 |
| Number = 25.370 | = 25 + 3/10 + 7/100 + 0/1000 | |||||
3. Decimal and fraction examples
- 0.1 = 1 tenth = 1/10
- 0.25 = 25 hundredths = 25/100 = 1/4
- 2.05 = 2 + 5 hundredths = 2 + 5/100
4. Number line (showing decimals)
Example: 0.7 is 7 tenths โ shown by the red dot.
5. Converting common fractions to decimals
- Fractions with denominator 10 or 100 are easy:
- 3/10 = 0.3
- 47/100 = 0.47
- Sometimes divide numerator by denominator:
1 รท 4 = 0.25, so 1/4 = 0.25
6. Adding and subtracting decimals
Always line up the decimal points (place-value alignment). Fill empty places with zeros if needed.
Example: 3.45 + 12.7
3.45
12.70
-----
16.15
Explanation: 12.7 is written as 12.70 to match hundredths place. 5 + 0 = 5; 4 + 7 = 11 (write 1, carry 1) โฆ
12.70
-----
16.15
7. Multiplying and dividing by 10, 100, 1000
- Multiply by 10: move decimal 1 place to the right. Example: 2.34 ร 10 = 23.4
- Multiply by 100: move decimal 2 places to the right. Example: 0.7 ร 100 = 70
- Divide by 10: move decimal 1 place to the left. Example: 45 รท 10 = 4.5
8. Rounding decimals
To round to a place (e.g., nearest tenth), look at the next digit:
- Round 3.46 to nearest tenth: look at hundredths (6) โ increase tenths (4) by 1 โ 3.5
- Round 2.141 to nearest hundredth: look at thousandths (1) โ keep hundredths as 14 โ 2.14
9. Comparing and ordering decimals
Compare place by place, starting with whole numbers. If whole parts are same, compare tenths, then hundredths, etc.
Example: Order 0.75, 0.7, 0.705 from smallest to largest.
0.700, 0.705, 0.750 โ so smallest is 0.7, then 0.705, then 0.75
10. Real-life examples (Kenyan context)
- Money: KSh 52.50 means 52 shillings and 50 cents (or 50 hundredths of a shilling).
- Measurement: 1.25 m = 1 metre and 25 centimetres (since 0.25 m = 25 cm).
- Fuel: Filling 12.6 L of petrol means twelve litres and six tenths of a litre.
11. Practice questions
- Write as a decimal: 7 tenths + 3 hundredths.
- Change to a fraction (simple): 0.4 and 0.75.
- Add: 6.25 + 3.6
- Subtract: 15.0 โ 4.37
- Multiply: 0.8 ร 10
- Divide: 45 รท 100
- Round 3.678 to the nearest tenth.
- Order from smallest to largest: 1.02, 1.2, 1.005
- A packet of sugar costs KSh 38.75. You buy 2 packets. How much do you pay?
- Convert 3/4 to a decimal.
12. Answers
- 0.73 (7 tenths = 0.7; 3 hundredths = 0.03 โ 0.7 + 0.03 = 0.73)
- 0.4 = 4/10 = 2/5; 0.75 = 75/100 = 3/4
- 6.25 + 3.6 = 6.25 + 3.60 = 9.85
- 15.00 โ 4.37 = 10.63
- 0.8 ร 10 = 8.0
- 45 รท 100 = 0.45
- 3.678 โ nearest tenth is 3.7 (because hundredths = 7 โ round up)
- Rewrite with same places: 1.020, 1.005, 1.200 โ order: 1.005, 1.02, 1.2
- 2 ร KSh 38.75 = KSh 77.50
- 3/4 = 0.75
Tip for learners: Practice lining up decimal points when adding or subtracting. Use real coins and measurements (metre stick, jerrycan) to see decimals in real life.
Created for Kenyan upper primary learners โ teacher may copy and print these notes for classroom use.