Grade 5 Mathematics Numbers – Decimals Notes

Mathematics — Numbers

Subtopic: Decimals (for age 10)

Decimals are another way to write parts of whole numbers. We use a decimal point (.) to show the whole part and the fractional part. Decimals are often used for money, length and measuring.

How to read and write decimals

• 3.7 is read "three point seven" or "three and seven tenths". It means 3 + 7/10.
• 4.25 is "four point two five" or "four and twenty-five hundredths". It means 4 + 2/10 + 5/100.
• 0.6 is "zero point six" or "six tenths".

Comparing and ordering decimals

To compare decimals, look at the whole number first. If equal, compare tenths, then hundredths, etc.

Adding and subtracting decimals

Always line up the decimal points before you add or subtract. You can add zeros at the end to make the same number of decimal places.

Multiply or divide by 10, 100, 1000

• Multiply by 10: move decimal point one place to the right. Example: 2.3 × 10 = 23.
• Multiply by 100: move point two places right. 0.45 × 100 = 45.
• Divide by 10: move point one place left. 35.7 ÷ 10 = 3.57.

Rounding decimals

To round to the nearest whole number, look at the tenths place:

• If tenths is 0–4, round down (keep whole number).
• If tenths is 5–9, round up (add 1 to whole number).

Example: 4.3 ≈ 4 (nearest whole number). 4.7 ≈ 5.

Rounding to nearest tenth: look at hundredths (0–4 down, 5–9 up). Example: 3.456 ≈ 3.46 (to 2 decimal places).

Real life examples (Kenya)

• Money: KSh 125.50 means 125 shillings and 50 cents.
• Length: 1.5 m = 1 metre and 50 centimetres (0.5 m = 50 cm).
• Weighing: 2.25 kg = 2 kilograms and 250 grams.

Practice questions

1. Write 7 tenths as a decimal.
2. Convert 45/100 to a decimal.
3. Which is larger: 6.03 or 6.3?
4. Add: 2.75 + 1.4
5. Subtract: 10.0 − 3.47
6. Round 3.76 to the nearest whole number.
7. Multiply 0.8 by 10.
8. Write 1 metre 20 cm as a decimal in metres.
9. Convert 3/1000 to a decimal.
10. Order these from smallest to largest: 0.5, 0.45, 0.55.

Tip: Practise by using real items — count money, measure lengths at home, and try writing those measurements as decimals.