Grade 6 Mathematics Numbers – Decimals Notes

Mathematics — Numbers: Decimals

Age: 11 (Kenyan upper primary)

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:

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)

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 ÷ 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.

7. Multiplying and dividing by 10, 100, 1000

• Multiply by 10: move decimal 1 place to the right. Example: 2.34 × 10 = 23.4
• Multiply by 100: move decimal 2 places to the right. Example: 0.7 × 100 = 70
• Divide by 10: move decimal 1 place to the left. Example: 45 ÷ 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) → increase tenths (4) by 1 → 3.5
• Round 2.141 to nearest hundredth: look at thousandths (1) → keep hundredths as 14 → 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.

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

1. Write as a decimal: 7 tenths + 3 hundredths.
2. Change to a fraction (simple): 0.4 and 0.75.
3. Add: 6.25 + 3.6
4. Subtract: 15.0 − 4.37
5. Multiply: 0.8 × 10
6. Divide: 45 ÷ 100
7. Round 3.678 to the nearest tenth.
8. Order from smallest to largest: 1.02, 1.2, 1.005
9. A packet of sugar costs KSh 38.75. You buy 2 packets. How much do you pay?
10. Convert 3/4 to a decimal.

12. Answers

1. 0.73 (7 tenths = 0.7; 3 hundredths = 0.03 → 0.7 + 0.03 = 0.73)
2. 0.4 = 4/10 = 2/5; 0.75 = 75/100 = 3/4
3. 6.25 + 3.6 = 6.25 + 3.60 = 9.85
4. 15.00 − 4.37 = 10.63
5. 0.8 × 10 = 8.0
6. 45 ÷ 100 = 0.45
7. 3.678 → nearest tenth is 3.7 (because hundredths = 7 → round up)
8. Rewrite with same places: 1.020, 1.005, 1.200 → order: 1.005, 1.02, 1.2
9. 2 × KSh 38.75 = KSh 77.50
10. 3/4 = 0.75