Instructions
Read each question carefully and write your answers in the spaces provided. Show your working where necessary. Good luck!
3. Significant Figures
Complete the table by rounding each number to one significant figure (1 s.f.) and then to two significant figures (2 s.f.).
| Original Number | Round to 1 s.f. | Round to 2 s.f. |
|---|---|---|
| 45,678 | ||
| 0.00983 | ||
| 6.7421 | ||
| 298.5 |
4. Mixed Rounding Challenge
Choose one of the following real-life scenarios and solve it in the space below. Show your rounding and your calculations.
A) A car costs £12,784. Round the price to the nearest £10, the nearest £100, and the nearest £1,000.
B) A stadium holds a maximum of 38,947 people. For a big match, it’s about three-quarters full. Estimate how many tickets were sold by first rounding the stadium's capacity.
Your chosen scenario (A or B):
5. Word Problem: Shopping Trip
You are buying a new phone, headphones, and a case. The prices are:
- Phone: £349.99
- Headphones: £87.65
- Case: £12.49
Part 1: Estimate the total cost. Round each item's price to the nearest pound (or another sensible number) before adding them together.
Your working for the estimate:
Estimated Total:
Part 2: Now, work out the exact total cost.
Exact Total:
Part 3: Was your estimate close to the exact total? Explain briefly.
6. Spot the Mistake
A fellow student says:
“To round 2,947.2 to the nearest 100, you look at the 4 and round down to 2,900.”
Their final answer is correct, but their explanation is not quite right. Explain what is wrong with their reasoning and give the correct way to think about it.
7. Reflection
Write 2 sentences about why rounding and estimation are useful skills in everyday life. Think about examples like shopping, building, cooking, or travel.
Answer Key
3. Significant Figures
| Original Number | Round to 1 s.f. | Round to 2 s.f. |
|---|---|---|
| 45,678 | 50,000 | 46,000 |
| 0.00983 | 0.01 | 0.0098 |
| 6.7421 | 7 | 6.7 |
| 298.5 | 300 | 300 |
4. Mixed Rounding Challenge
A) Nearest £10: £12,780. Nearest £100: £12,800. Nearest £1,000: £13,000.
B) Round 38,947 to 40,000. One-quarter of 40,000 is 10,000. So, three-quarters is 3 x 10,000 = 30,000. Estimate: About 30,000 tickets were sold. (Other reasonable rounding, like to 39,000, is also acceptable).
5. Word Problem: Shopping Trip
Estimated Total (example): £350 + £88 + £12 = £450. (Or £350 + £90 + £10 = £450).
Exact Total: £349.99 + £87.65 + £12.49 = £450.13.
Comparison: Yes, the estimate was very close to the exact total, only off by 13p.
6. Spot the Mistake
Example Explanation: The student is wrong because you don't look at the '4' to decide to round 'down'. To round to the nearest 100, you identify the hundreds digit (9) and look at the digit to its right (the 4 in the tens place). Because 4 is less than 5, the hundreds digit (9) stays the same, and the following digits before the decimal point become zeros. The '4' tells you what to do, but it isn't what is being rounded.
7. Reflection
Example Answers (answers will vary):
1. Estimation is useful when shopping to get a quick idea of the total bill to make sure you have enough money.
2. Rounding is important in travel to estimate journey times, helping you plan when to leave so you aren't late.