Mathematics • Year 8 • Unit 1 • Lesson 2
Converting FDP in the Real World
Use the conversion methods from Lesson 2 in everyday contexts: comparing test marks, splitting a bill, reading a fuel gauge, and converting recipe ratios. Then explain your method in your own words.
1. Word problems
Each problem uses a conversion from Lesson 2: fraction → decimal → percentage, or back the other way. Show your working — a single final answer with no working only earns half marks.
1.1 — Test mark face-off. Your test score is 17/20. Your friend's score is 0.88.
(a) Convert 17/20 to a decimal.
(b) Convert your friend's decimal to a percentage.
(c) Who did better? 3 marks
1.2 — Splitting a bill three ways. Three friends split a $90 pizza bill equally.
(a) Write each friend's share as a fraction of the bill.
(b) Convert that fraction to a decimal (use recurring notation).
(c) How many dollars does each friend owe? 3 marks
1.3 — Fuel gauge. Mum's car fuel gauge reads 3/8 of a tank. The car's display shows it as a percentage.
(a) Convert 3/8 to a decimal (use long division — denominator 8 has only 2s, so it will terminate).
(b) Convert that decimal to a percentage.
(c) If a full tank is 60 L, how many litres of fuel are left? 3 marks
1.4 — Recipe scaling. A muffin recipe needs 2/5 of a cup of sugar. The packet shows quantities in decimals.
(a) Convert 2/5 to a decimal.
(b) Convert the same fraction to a percentage of a cup.
(c) If you make 3× the recipe, how much sugar (in decimal cups) is that in total? 3 marks
1.5 — Survey percent. In a Year 8 survey, 18 of 24 students said they have a pet.
(a) Write the result as a fraction, then simplify.
(b) Convert that simplified fraction to a decimal.
(c) Convert to a percentage. 3 marks
2. Explain your thinking
This question is about communication, not just answers. Use full sentences. 4 marks
2.1 A classmate divides 1 by 7 on a calculator and sees 0.142857142857... on the screen. They write down 1/7 ≈ 0.14. In your own words, explain (i) why their decimal is a rounded approximation, not exact, (ii) what kind of decimal 1/7 actually produces, and (iii) how to write it correctly using recurring notation. Use the word "remainder" somewhere in your answer.
How did this worksheet feel?
What I'll revisit before next class:
1.1 — Test mark face-off
(a) 17 ÷ 20 = 0.85.
(b) 0.88 × 100 = 88%.
(c) 0.88 > 0.85, so your friend did better (88% vs 85%).
1.2 — Splitting a bill three ways
(a) Each share = 1/3 of the bill.
(b) 1 ÷ 3 = 0.3̄ (recurring).
(c) 1/3 of $90 = $90 ÷ 3 = $30 each.
Note: although 1/3 as a decimal is messy, 1/3 of $90 comes out perfectly clean.
1.3 — Fuel gauge
(a) 3 ÷ 8 = 0.375.
(b) 0.375 × 100 = 37.5%.
(c) 0.375 × 60 = 22.5 L left in the tank.
1.4 — Recipe scaling
(a) 2 ÷ 5 = 0.4.
(b) 0.4 × 100 = 40% of a cup.
(c) 0.4 × 3 = 1.2 cups of sugar.
1.5 — Survey percent
(a) 18/24. HCF of 18 and 24 is 6, so 18/24 = 3/4.
(b) 3 ÷ 4 = 0.75.
(c) 0.75 × 100 = 75% of students have a pet.
2.1 — Explain your thinking (sample response)
When you divide 1 by 7 you get a never-ending decimal: each remainder feeds back into the next step of the division, and because the only possible non-zero remainders when you divide by 7 are 1, 2, 3, 4, 5 and 6, after six steps a remainder must repeat — and the digits then repeat too. So 1/7 produces a recurring decimal, not a terminating one. Rounding to 0.14 throws away most of the repeating block, so it's an approximation, not the true value. Written exactly with recurring notation, 1/7 = 0.142857 — the bar over 142857 means that whole block repeats forever.
Marking: 1 mark for naming "recurring decimal"; 1 mark for explaining why with "remainder"; 1 mark for the correct recurring notation; 1 mark for a clear full-sentence response.