Grade 7 Mathematics NUMBERS – Decimals Notes

Mathematics — NUMBERS

Subtopic: Decimals (Age 12 — Kenya)

What is a decimal?
A decimal is a way of writing numbers that are between whole numbers. It uses a decimal point (.) to separate the whole number part from the fractional part.

Place value for decimals

Digits left of the decimal point are whole numbers (hundreds, tens, ones). Digits right of the point are parts of one (tenths, hundredths, thousandths...).

Converting between decimals and fractions

• Decimal to fraction: Put the digits after the point over the corresponding power of 10, then simplify.
  0.75 = 75/100 = 3/4
• Fraction to decimal: Divide numerator by denominator or write as parts of 10, 100, 1000 when possible.
  3/4 = 3 ÷ 4 = 0.75

Comparing and ordering decimals

Line up the decimal points and compare digits from left to right. If needed, add zeros to make the same number of decimal places.

Rounding decimals

To round to a certain place (ones, tenths, hundredths), look at the next digit:

• If the next digit is 0–4, keep the place the same and drop digits after it.
• If the next digit is 5–9, increase the place by 1 and drop digits after it.

Adding and subtracting decimals

Always line up decimal points vertically. Add zeros if needed so each column has a digit.

Multiplying decimals

Multiply ignoring decimal points. Count total decimal places in both numbers. Place decimal point in the product so it has that many decimal places.

Dividing by decimals

If the divisor is not a whole number, move the decimal point right in both divisor and dividend the same number of places to make the divisor whole, then divide as usual.

Decimals in everyday Kenyan contexts

• Money: KSh 45.50 means 45 shillings and 50 cents (or 50 hundredths of a shilling).
• Distance: 2.75 km = 2 kilometres and 750 metres (0.75 km = 750 m).
• Mass: 1.25 kg = 1 kg and 250 g.

Simple visual: showing 0.7 as part of 1

Quick rules to remember

• Always line up decimal points when adding/subtracting.
• For multiplication, count decimal places then place the point in the product.
• To divide by a decimal, first make the divisor a whole number by shifting the decimal.
• Fill with zeros to compare or to line up digits (e.g., 3.6 = 3.60).

Practice questions

1. Write 4.2 as a fraction. (Answer: 42/10 = 21/5)
2. Order these from smallest to largest: 0.5, 0.45, 0.505. (Answer: 0.45, 0.5, 0.505)
3. Round 6.378 to the nearest hundredth. (Answer: 6.38)
4. Calculate: 3.25 + 2.4 = ? (Answer: 5.65)
5. Calculate: 0.6 × 0.05 = ? (Answer: 0.03)