Mathematics • Year 7 • Unit 1 • Lesson 10
Decimals — Mixed Challenge
Pull every Lesson 10 idea together: identify place values, compare and order decimals, round to a chosen place, convert between fractions and decimals, and spot a classic "rounded the wrong digit" mistake. End with an open puzzle.
1. Mixed problems — choose the right idea
Each question uses a different part of Lesson 10. Decide which idea applies before you start writing. Show your working. 2 marks each
1.1 In 7.0925, what is the value of the digit 9, and what is the value of the digit 5?
1.2 Place >, < or = between each pair:
(a) 0.305 ____ 0.35 (b) 1.020 ____ 1.2 (c) 4.70 ____ 4.7
1.3 Round 12.4567 to (a) 1 d.p. and (b) 3 d.p.
1.4 Order from smallest to largest: 0.6, 0.06, 0.66, 0.606.
1.5 Convert 0.65 to a fraction in simplest form.
1.6 Round 0.9961 to 2 decimal places. (Careful — the rounding will carry over into the tenths.)
2. Find the mistake
Another Year 7 student has tried to round 4.2956 to 2 decimal places. Their working is shown below. Exactly one line contains a mistake. Spot it, explain why it's wrong, then re-do the working correctly. 3 marks
Student's working — round 4.2956 to 2 d.p.:
Line 1: 2 d.p. means I want exactly 2 digits after the decimal point.
Line 2: Target digit (hundredths) = 9.
Line 3: To decide rounding, look at the last digit: 6. Since 6 ≥ 5, round up.
Line 4: Round 9 up: 9 + 1 = 10 — carry the 1 into the tenths column.
Line 5: Answer: 4.30.
(a) Which line contains the mistake?
(b) Explain in one or two sentences why that line is wrong.
(c) Write out the corrected working in full, including the corrected final answer.
Stuck? The rounding rule says "look at the digit immediately to the right of the target". Not the last digit overall.3. Open-ended challenge — decimals that round the same
This question has more than one correct answer. Show three that work and explain. 4 marks
3.1 Find three different decimals that all round to 5.4 when rounded to 1 decimal place.
For each one, show why it rounds to 5.4 by finding the target digit and the next digit.
Bonus: What is the smallest decimal and the largest decimal that round to 5.4 to 1 d.p.? Explain the range in words.
How did this worksheet feel?
What I'll revisit before next class:
1.1 — Values of 9 and 5 in 7.0925
The 9 is in the hundredths place, so its value is 0.09. The 5 is in the ten-thousandths place, so its value is 0.0005.
1.2 — Compare
(a) 0.305 vs 0.35 = 0.350. Tenths tie (3); hundredths 0 vs 5: 0.305 < 0.35.
(b) 1.020 vs 1.2 = 1.200. Tenths 0 vs 2: 1.020 < 1.2.
(c) 4.70 = 4.7 (trailing zero doesn't change value).
1.3 — Round 12.4567
(a) 1 d.p.: target = 4, next = 5. 5 ≥ 5, round up: 12.5.
(b) 3 d.p.: target = 6 (thousandths), next = 7. 7 ≥ 5, round up: 12.457.
1.4 — Order 0.6, 0.06, 0.66, 0.606
Write as 0.600, 0.060, 0.660, 0.606. Tenths: 6, 0, 6, 6 → 0.060 smallest.
Among 0.600, 0.660, 0.606: hundredths split 0.660 (6) above the others, and 0.600 vs 0.606: thousandths 0 vs 6 → 0.600 < 0.606.
Order: 0.06 < 0.6 < 0.606 < 0.66.
1.5 — Convert 0.65 to a fraction
0.65 = 65/100. HCF(65, 100) = 5. 65 ÷ 5 = 13, 100 ÷ 5 = 20. So 13/20.
1.6 — Round 0.9961 to 2 d.p.
Target = 9 (hundredths). Next digit = 6. 6 ≥ 5, so 9 rounds up → 9 + 1 = 10. Carry the 1 into the tenths: 9 in tenths + 1 = 10 → that carries into the ones: 0 + 1 = 1, and tenths becomes 0.
Answer: 1.00 (keep both trailing zeros to show 2 d.p.).
2 — Find the mistake
(a) The mistake is on Line 3.
(b) The rounding rule says to look at the digit immediately to the right of the target, not the last digit overall. The target is the hundredths (9), so we should look at the thousandths (5), not the ten-thousandths (6).
(c) Corrected working:
Line 3 (fixed): Look at the thousandths digit (the one right after the target): 5. Since 5 ≥ 5, round up.
(The rounding decision happens to be the same in this case because both 5 and 6 are ≥ 5.) The final answer of 4.30 is still correct, but only because both digits trigger rounding up. In other examples this slip-up would give a wrong answer.
3 — Decimals that round to 5.4 (sample solution)
Three valid examples: 5.41 (target 4, next 1; 1 < 5, 4 stays); 5.36 (target 3, next 6; 6 ≥ 5, 3 rounds up to 4); 5.42 (target 4, next 2; 2 < 5, 4 stays). All three round to 5.4 to 1 d.p.
Bonus: The smallest decimal that rounds to 5.4 is 5.35 (the rule is normally "5 rounds up", so 5.35 → 5.4). The largest decimal that rounds to 5.4 is anything just below 5.45 — e.g. 5.4499…. So the range is 5.35 ≤ x < 5.45. Any value in that range rounds to 5.4 to 1 d.p.
Marking: 2 marks for three valid examples with target/next-digit working shown; 1 mark for the lower bound (5.35); 1 mark for the upper bound (just below 5.45) and the range statement.