Decimals and Percentages

Decimals and percentages appear throughout the CSSE maths paper, from straightforward calculations to multi-step word problems involving money, measures, and discounts. This lesson covers everything you need to know.

---

Understanding Decimals

Decimals use a decimal point to separate whole numbers from parts of a whole.

Ones	.	Tenths	Hundredths	Thousandths
3	.	4	7	5

The number 3.475 means: 3 + 4/10 + 7/100 + 5/1000.

---

Adding and Subtracting Decimals

Line up the decimal points and work column by column, just like with whole numbers.

Worked Example

Calculate 14.63 + 8.7

Write 8.7 as 8.70, then add:

	T	O	.	t	h
	1	4	.	6	3
+	0	8	.	7	0
=	2	3	.	3	3

Answer: 23.33

---

Multiplying Decimals

Multiplying by a whole number

Ignore the decimal point, multiply as whole numbers, then put the decimal point back.

Worked Example

Calculate 3.45 × 6

• 345 × 6 = 2,070
• 3.45 has 2 decimal places, so put the point back: 20.70 = 20.7

Multiplying by 10, 100, 1000

Operation	Rule	Example
× 10	Move digits 1 place left	3.45 × 10 = 34.5
× 100	Move digits 2 places left	3.45 × 100 = 345
× 1000	Move digits 3 places left	3.45 × 1000 = 3,450

Dividing by 10, 100, 1000

Operation	Rule	Example
÷ 10	Move digits 1 place right	345 ÷ 10 = 34.5
÷ 100	Move digits 2 places right	345 ÷ 100 = 3.45
÷ 1000	Move digits 3 places right	345 ÷ 1000 = 0.345

CSSE Tip: Questions that involve multiplying or dividing by powers of 10 appear often. Make sure you move the digits the correct number of places — it is the digits that move, not the decimal point!

---

Understanding Percentages

Per cent means out of 100. So 45% means 45 out of 100, which is the same as 45/100 or 0.45.

---

Converting Between Fractions, Decimals, and Percentages