Grade 7 — Cambridge Lower Secondary Stage 7, Unit 4. Master multiplying and dividing decimals, spot the difference between terminating and recurring decimals, and use decimals in real-world problems.
Key Vocabulary
Terminating decimal — ends after a finite number of digits. e.g. 0.75
Recurring decimal — one or more digits repeat forever. e.g. 0.3333… = 0.3
Dot notation — a dot above a digit shows it repeats; two dots show the start and end of the repeating block.
Multiplying Decimals by Decimals — Grid Method
Watch how 2.4 × 1.3 is built step by step in the grid below:
Grid for 2.4 × 1.3
×
2
0.4
1
0.3
Watch the grid fill in...
Steps:
1. Split each number into whole + decimal parts.
2. Multiply each pair and fill each cell.
3. Add all four cells to get the answer.
Dividing Decimals by Decimals
The Rule: Multiply both numbers by 10 (or 100) until the divisor is a whole number, then divide normally.
Example: 3.6 ÷ 0.4 → multiply both by 10 → 36 ÷ 4 = 9
3.6 ÷ 0.4 → ×10 both → 36 ÷ 4 = 9
0.12 ÷ 0.04 → ×100 both → 12 ÷ 4 = 3
Recurring Decimals from Fractions
Method: Perform long division. If the remainder repeats, the decimal is recurring.
A fraction in lowest terms gives a terminating decimal only if its denominator has no prime factors other than 2 and 5.
Fraction
Decimal
Type
1/3
0.3
Recurring
1/7
0.142857
Recurring (6-digit cycle)
2/9
0.2
Recurring
3/4
0.75
Terminating
7/20
0.35
Terminating
Decimal to Fraction — How to Simplify
0.6 = 610 = 35 (divide top and bottom by 2)
0.35 = 35100 = 720 (divide by 5)
0.125 = 1251000 = 18 (divide by 125)
Ordering Decimals Including Negatives
Remember: Negative numbers to the left of zero are smaller. −2.5 < −1.3 < 0 < 0.8 < 1.2
Line up decimal points when comparing. Fill gaps with zeros: 1.4 = 1.40 = 1.400
Worked Examples
Study these carefully before tackling the exercises.
Example 1: Multiply Decimal × Decimal (Grid Method)
Check: 32 × 24 = 768 → two decimal places total → 7.68 ✓
Example 2: Divide Decimal by Decimal
Question: Calculate 5.6 ÷ 0.07
Step 1: The divisor is 0.07. It needs to become a whole number → multiply by 100.
Step 2: Multiply both numbers by 100: 5.6 × 100 = 560 0.07 × 100 = 7
Step 3: Now divide: 560 ÷ 7 = 80
Answer: 5.6 ÷ 0.07 = 80
Check: 80 × 0.07 = 5.6 ✓
Example 3: Convert Fraction to Recurring Decimal (Dot Notation)
Question: Write 59 as a recurring decimal using dot notation.
Step 1: Divide 5 by 9 using long division:
5.000... ÷ 9: 9 goes into 50 five times remainder 5 → keeps repeating.
Step 2: 5 ÷ 9 = 0.5555... = 0.5
Answer:59 = 0.5
A single dot above the digit means that digit repeats forever.
Example 4: Convert Terminating Decimal to Fraction (Simplest Form)
Question: Write 0.48 as a fraction in its simplest form.
Step 1: 0.48 has two decimal places → write as 48100
Step 2: Find HCF of 48 and 100 → HCF = 4
Step 3: Divide top and bottom by 4 → 1225
Answer: 0.48 = 1225
25 = 5² → only prime factor is 5 → terminating ✓
Decimal Multiplier — Grid Visualizer
Enter two decimals (up to 2 d.p. each). Click Calculate to see the grid method with coloured cells.
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How the Grid Works
Each decimal is split into its whole-number part and its decimal part (tenths or hundredths). The four cells of the grid show the four partial products. Adding them gives the exact answer — no rounding needed!
Exercise 1 — Decimal × Decimal
Calculate each product. Type your answer in the box, then click Check All.
Exercise 2 — Dividing by Decimals
For each question, complete the converted form (multiply both by 10 or 100), then write the final answer.
Exercise 3 — Fraction to Decimal
For each fraction: click Terminating or Recurring, then type the decimal. Click Check All.
Exercise 4 — Decimal to Fraction
Write each decimal as a fraction in its simplest form. Enter the numerator and denominator. Click Check All.
Exercise 5 — Ordering Decimals
Click the numbers in ascending order (smallest first). Check each set when done.
Exercise 6 — Multi-Step Word Problems
Work through each problem one at a time. Type your answer and click Check.
Practice Questions
Write your working on paper!
Calculate 1.2 × 3.4
Calculate 4.5 × 2.6
Calculate 0.7 × 0.9
Calculate 3.8 × 1.5
Calculate 6.3 × 0.04
Calculate 7.2 ÷ 0.9
Calculate 4.8 ÷ 0.6
Calculate 3.5 ÷ 0.07
Calculate 0.84 ÷ 0.04
Calculate 2.16 ÷ 0.08
Write 13 as a decimal using dot notation.
Write 29 as a decimal using dot notation.
Write 16 as a decimal using dot notation.
Write 511 as a decimal using dot notation.
Write 0.75 as a fraction in simplest form.
Write 0.64 as a fraction in simplest form.
Write 0.125 as a fraction in simplest form.
Arrange in ascending order: −1.5, 0.8, −0.3, 1.2, −2.1, 0.09
A plank is 2.4 m long. It is cut into pieces each 0.08 m long. How many pieces are there?
Petrol costs $1.35 per litre. How much does 4.6 litres cost? Give your answer to the nearest cent.
1.2 × 3.4 = 4.08
4.5 × 2.6 = 11.70
0.7 × 0.9 = 0.63
3.8 × 1.5 = 5.70
6.3 × 0.04 = 0.252
7.2 ÷ 0.9 → 72 ÷ 9 = 8
4.8 ÷ 0.6 → 48 ÷ 6 = 8
3.5 ÷ 0.07 → 350 ÷ 7 = 50
0.84 ÷ 0.04 → 84 ÷ 4 = 21
2.16 ÷ 0.08 → 216 ÷ 8 = 27
0.3
0.2
0.16
0.45 (0.454545... = 0.45)
0.75 = 75/100 = 3/4
0.64 = 64/100 = 16/25
0.125 = 125/1000 = 1/8
−2.1, −1.5, −0.3, 0.09, 0.8, 1.2
2.4 ÷ 0.08 → 240 ÷ 8 = 30 pieces
1.35 × 4.6 = $6.21
Challenge — Hard Word Problems
Show all working on paper. These are multi-step!
A car travels at 56.4 km/h for 2.5 hours. How far does it travel?
A rectangular field is 12.4 m wide and 8.5 m long. What is the area? A fence costs $3.60 per metre. What is the total cost of fencing all four sides?
A baker buys 4.8 kg of flour at $0.85 per kg and 1.6 kg of sugar at $1.20 per kg. What is the total cost?
A water tank holds 36.8 litres. Water drains out at 0.08 litres per second. How many seconds does it take to empty?
Write 712 as a decimal (using dot notation). Explain why it is recurring, not terminating.
Three friends share a bill of $47.61 equally. How much does each person pay? Is the answer a terminating or recurring decimal?
A rope is 5.76 m long. Pieces of length 0.32 m are cut from it. How many complete pieces can be cut, and how much rope is left over?
In a science experiment, a reading of −3.7 is recorded, then the value increases by 5.2, then decreases by 0.85. What is the final reading?
A shop sells pens at $0.65 each and rulers at $0.90 each. Yusuf spends exactly $5.80 and buys more pens than rulers. How many of each did he buy?
A train journey is 124.8 km. The first part is 0.375 of the total distance. How long (in km) is the first part? Write 0.375 as a fraction in simplest form first.