Mathematics • Year 7 • Unit 1 • Lesson 10
Decimals in the Real World
Use decimals to read race times, work out the cost of food at the canteen, round measurements for a science experiment, and check whether two price tags show the same value.
1. Word problems
Each problem uses the decimal ideas from Lesson 10: place value, compare/order, round to a given number of decimal places, or convert between decimals and fractions. Show your working — a single answer with no working only earns half marks.
1.1 — Race times. Three Year 7 students timed their 50-metre run: Liam ran 8.65 seconds, Aisha ran 8.6 seconds, and Noah ran 8.605 seconds.
(a) Who was fastest? (Lowest time wins.)
(b) Order all three times from fastest to slowest. Show one column that decided each comparison. 3 marks
1.2 — Canteen lunch. Maya buys a sandwich for $4.75, a juice for $2.40, and a piece of fruit for $1.20. The cashier says the total comes to "about eight dollars and forty cents".
(a) Find the exact total.
(b) Round the exact total to the nearest dollar.
(c) Is the cashier's "about $8.40" estimate correct, an underestimate, or an overestimate? 3 marks
1.3 — Science experiment. Jordan measures the length of a leaf as 6.847 cm.
(a) Round 6.847 to 1 decimal place — what does the leaf length round to?
(b) Round 6.847 to 2 decimal places.
(c) In his lab book Jordan writes "6.85 cm" — what number of decimal places is that, and is it a correct rounding? 3 marks
1.4 — Price tags. Two shops both sell the same brand of milkshake. Shop A labels it $3.5; Shop B labels it $3.50.
(a) Are the two prices equal?
(b) Explain in one sentence what role the trailing zero plays in the price tag at Shop B. 2 marks
1.5 — Fraction to decimal. A recipe says use 3/4 cup of milk, but Aisha's measuring jug only shows decimals.
(a) Convert 3/4 to a decimal.
(b) Convert 1/8 to a decimal. (Hint: 8 × 125 = 1000.)
(c) Which is bigger, 3/4 or 0.7? Use the decimal forms to compare. 3 marks
2. Explain your thinking
This question is about communication, not just answers. Use full sentences. 4 marks
2.1 A Year 7 student says: "0.37 must be bigger than 0.4 because 37 is bigger than 4." Explain in your own words: (i) is the conclusion right or wrong, (ii) what mistake the student is making about decimals, (iii) what the correct method is for comparing two decimals. Use a money example (such as $0.37 vs $0.40) to back up your explanation.
How did this worksheet feel?
What I'll revisit before next class:
1.1 — Race times
Write all with 3 d.p.: 8.650, 8.600, 8.605.
(a) Lowest time wins: Aisha (8.600 s).
(b) Compare 8.605 and 8.650: tenths tie (6), hundredths 0 vs 5 → 8.605 < 8.650. Order fastest → slowest: Aisha (8.6) < Noah (8.605) < Liam (8.65). The hundredths column decided Noah vs Liam; the hundredths column decided Aisha vs Noah.
1.2 — Canteen lunch
(a) Total: 4.75 + 2.40 + 1.20 = $8.35.
(b) To nearest dollar: target = ones digit (8). Next digit = 3 (tenths). 3 < 5, so 8 stays. Rounded = $8.
(c) "About $8.40" is an overestimate (actual is $8.35, slightly less). Five cents over.
1.3 — Science experiment
(a) Round 6.847 to 1 d.p.: target = 8 (tenths), next = 4. 4 < 5, so 8 stays. = 6.8 cm.
(b) Round to 2 d.p.: target = 4 (hundredths), next = 7. 7 ≥ 5, so 4 rounds up to 5. = 6.85 cm.
(c) "6.85" is 2 decimal places, and yes, it is the correct rounding.
1.4 — Price tags
(a) Yes — $3.5 and $3.50 are equal. The trailing zero in $3.50 doesn't change the value.
(b) The trailing zero shows the price has been given to the nearest cent (2 decimal places). For money this is the normal convention, so customers know exactly how many cents to pay.
1.5 — Fraction to decimal
(a) 3/4 = (3 × 25)/(4 × 25) = 75/100 = 0.75.
(b) 1/8 = (1 × 125)/(8 × 125) = 125/1000 = 0.125.
(c) Compare 3/4 = 0.75 with 0.7 (= 0.70). Tenths: 7 = 7. Hundredths: 5 vs 0 → 0.75 > 0.70. So 3/4 is bigger than 0.7.
2.1 — Explain your thinking (sample response)
(i) The conclusion is wrong: 0.37 is smaller than 0.4, not bigger.
(ii) The student treated the digits after the decimal point as if they were whole numbers ("37 vs 4"). But position matters — the first digit after the point is tenths, the second is hundredths, and so on. A digit's value depends on its column, not on how many digits are written.
(iii) Correct method: write both decimals with the same number of decimal places by adding trailing zeros (0.37 and 0.40), then compare digit by digit from the left. Tenths: 3 vs 4 → 0.37 < 0.40.
Money check: $0.37 is 37 cents and $0.40 is 40 cents. 40 cents > 37 cents, so $0.40 (which is the same as $0.4) is bigger. The student's reasoning would also wrongly suggest that $0.99 > $1, which is clearly false.
Marking: 1 for saying conclusion is wrong; 1 for naming the place value mistake; 1 for the "add trailing zeros and compare left to right" method; 1 for a clear money example.