GRADE 8 Mathematics NUMBERS – Decimals Notes
MATHEMATICS — NUMBERS
Subtopic: Decimals (Age 13 — Kenyan context)
Learning objectives
- Read and write decimal numbers and know place values (tenths, hundredths, thousandths).
- Convert between fractions and decimals.
- Compare, order and round decimal numbers.
- Add, subtract, multiply and divide decimals correctly.
- Apply decimals to everyday Kenyan contexts (money, length, mass, fuel).
1. Place value with decimals
A decimal number has a decimal point (.) that separates whole-number part from fractional part.
Visual: Tenths (10 equal parts)
0.3 means 3 out of 10 parts. (Each box = 1/10)
2. Writing and reading decimals
- 245.6 — read as "two hundred and forty-five point six" or "two hundred and forty-five and six tenths".
- 0.08 — read as "eight hundredths".
- 3.125 — read as "three point one two five" or "three and one hundred and twenty-five thousandths".
3. Convert between fractions and decimals
Fraction to decimal: divide numerator by denominator.
1/2 = 1 ÷ 2 = 0.5 (or 0.50)
7/100 = 0.07
Decimal to fraction: write the decimal as parts over 10, 100, 1000 then simplify.
0.75 = 75/100 = 3/4
0.125 = 125/1000 = 1/8
4. Comparing and ordering decimals
Line the numbers up by decimal point. Look at the whole number first; if equal, compare tenths, then hundredths, etc.
Whole parts both 3. Compare tenths: 5 vs 5 (same). Hundredths: 6 vs 0 → 3.56 is larger.
5. Rounding decimals
Rules: look at the digit to the right of the place you round to.
- If it's 0–4, round down (keep digit). If 5–9, round up (add 1).
Round 6.478 to nearest whole number → 6 (because 0.478 < 0.5).
Round 6.678 to nearest whole number → 7 (because 0.678 ≥ 0.5).
Round 3.146 to 1 decimal place → 3.1 (look at hundredths: 4 → round down).
Round 3.146 to 2 decimal places → 3.15 (look at thousandths: 6 → round up).
6. Operations with decimals
Addition and subtraction
Write numbers so decimal points line up, add zeros if needed.
Align: 12.500
+3.275
=15.775
Multiplication
Multiply as whole numbers, then place the decimal point: total decimal places = sum of decimal places in factors.
Division
Shift decimal in divisor to make it a whole number (multiply both divisor and dividend by same power of 10), then divide.
7. Decimals in Kenyan real life
- Money: Ksh 245.50 means 245 shillings and 50 cents (50/100 of a shilling if using decimals for cents).
- Length: 1.25 m = 1 metre and 25 centimetres (because 0.25 m = 25 cm).
- Fuel: Filling 12.4 litres of petrol; price calculations use decimals.
- Mass: 0.75 kg = 750 g.
8. Worked examples
7 ÷ 8 = 0.875
Example 2 — Money: A shirt costs Ksh 799.90. You pay Ksh 1,000. How much change?
1000.00 − 799.90 = 200.10 → Ksh 200.10
Example 3 — Multiply: 3.75 × 0.2.
375 × 2 = 750. Decimal places 3 + 1 = 4 → 0.0750 = 0.075.
9. Practice questions
- Write as decimals: (a) 3/5 (b) 11/25
- Write as fractions in simplest form: (a) 0.4 (b) 0.875
- Order from smallest to largest: 0.305, 0.35, 0.3
- Round 4.678 to: (a) nearest whole number (b) one decimal place (c) two decimal places
- Calculate: (a) 12.75 + 3.6 (b) 5.2 × 0.6 (c) 7.5 ÷ 0.25
- Real-life: A litre of milk costs Ksh 92.50. How much for 3.5 litres?
- Convert: 0.65 m to centimetres.
- Convert to decimal: 37/50.
Answers
1b) 11/25 = 0.44
2a) 0.4 = 4/10 = 2/5
2b) 0.875 = 875/1000 = 7/8
3) Smallest → largest: 0.3, 0.305, 0.35
4a) 5 (nearest whole number)
4b) 4.7 (one decimal place)
4c) 4.68 (two decimal places)
5a) 12.75 + 3.6 = 16.35
5b) 5.2 × 0.6 = 3.12
5c) 7.5 ÷ 0.25 = 30
6) 92.50 × 3.5 = 323.75 → Ksh 323.75
7) 0.65 m = 65 cm
8) 37/50 = 0.74
Tip: Practise lining up decimal points when adding/subtracting. Use fractions division to change between forms. For exams (KCSE-style), show clear steps and write units (Ksh, m, L) where needed.