Measures and solids · Ages 13–14

Errors in measurement at work worksheet

Part of: Errors in measurement

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Measures and solids · Ages 13–14

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Write each answer in the space. For word problems, show your working and write a sentence answer.

1.A roll of ribbon is 39 m long, to the nearest 1 m. Each piece is to be 9 m long (to the nearest 1 m). At most how many pieces can be cut?
Answer:
2.14 bags of rice each weigh 29 kg to the nearest 1 kg. Their total weight W lies in kg ≤ W < kg.
Fill in each blank
Answer:
3.18 bags of rice each weigh 7 kg to the nearest 1 kg. Their total weight W lies in kg ≤ W < kg.
Fill in each blank
Answer:
4.A rectangular sheet is 28 cm by 11 cm, each to the nearest 1 cm. Its area A lies in cm² ≤ A < cm².
Fill in each blank
Answer:
5.A roll of wire is 39 m long, to the nearest 1 m; each piece is 4 m (to the nearest 1 m). Whatever the true lengths, how many pieces can always be cut, at least?
Answer:
6.A rectangular sheet is 18 cm by 30 cm, each to the nearest 1 cm. Its area A lies in cm² ≤ A < cm².
Fill in each blank
Answer:
7.A square tile's side is measured as 4 cm to the nearest 1 cm, so its area works out as 16 cm². By how many cm² is the area's upper limit more than 16 cm²?
Answer:
8.A triangle's sides, each to the nearest 0.1 cm, are 1.2 cm, 0.5 cm and 1.2 cm. What is the upper limit of its perimeter, in cm?
Answer:
9.A triangle's sides, each to the nearest 0.1 cm, are 1.1 cm, 0.8 cm and 1.4 cm. What is the upper limit of its perimeter, in cm?
Answer:

10.13 books each weigh 47 g to the nearest 1 g. Their total weight could be 617.5 g.
True or false?
Answer:
11.A rectangular flower bed is 5 m by 25 m, each to the nearest 1 m. Which of these could be its true perimeter?
- A. 57.5 m
- B. 62 m
- C. 62.5 m
- D. 61.5 m
Choose the right answer
Answer:
12.19 books each weigh 26 g to the nearest 1 g. Their total weight could be 484.5 g.
True or false?
Answer:

13.A lift can carry at most 872 kg. 15 people each weigh 58 kg to the nearest 1 kg. Taking the lift together, their total weight could be more than 872 kg.
True or false?
Working:
Answer:
14.A rectangular vegetable plot is 11.3 m by 8.7 m, each to the nearest 0.1 m. Its area S lies in m² ≤ S < m².
Fill in each blank
Working:
Answer:
15.A big bottle holds 2.1 L of juice (to the nearest 0.1 L). It is poured into cups of 250 mL each (to the nearest 10 mL). Whatever the true amounts, how many full cups can always be poured, at least?
Working:
Answer:
16.A wooden cube's edge is measured as 20 cm to the nearest 1 cm. By how many cm³ do the upper and lower limits of its volume differ?
Working:
Answer:
17.12 tiles each weigh 36 g to the nearest 1 g. Which of these could be their total weight?
- A. 438.5 g
- B. 438 g
- C. 435.25 g
- D. 425.5 g
Choose the right answer
Working:
Answer:
18.A corridor is 8 m long (to the nearest 1 m), and a row of square tiles, each 28 cm a side (to the nearest 1 cm), is laid along it. At most how many whole tiles fit in the row?
Working:
Answer:

Show the answers and working

Errors in measurement at work worksheet: Answers and working

1. 4 pieces
The ribbon is at most nearly 39.5 m and each piece at least 8.5 m: 39.5 ÷ 8.5 is just over 4, so at most 4 pieces (the decimals dropped).
2. 399, 413
Each bag is from 28.5 kg up to 29.5 kg: at least 14 × 28.5 = 399, less than 14 × 29.5 = 413.
3. 117, 135
Each bag is from 6.5 kg up to 7.5 kg: at least 18 × 6.5 = 117, less than 18 × 7.5 = 135.
4. 288.75, 327.75
Least: the lower limits multiplied, 27.5 × 10.5 = 288.75; greatest: the upper limits, 28.5 × 11.5 = 327.75 (the true area is less).
5. 8 pieces
The worst case: the wire at its shortest, 38.5 m, each piece nearly 4.5 m: 38.5 ÷ 4.5 is just over 8, so 8 pieces for sure.
6. 516.25, 564.25
Least: the lower limits multiplied, 17.5 × 29.5 = 516.25; greatest: the upper limits, 18.5 × 30.5 = 564.25 (the true area is less).
7. 4.25 cm²
The area's upper limit is 4.5 × 4.5 = 20.25, which is 20.25 − 16 = 4.25 cm² more: half a cm on the side makes far more on the area.
8. 3.05 cm
Each side's upper limit is 0.05 cm more, three of them 3 × 0.05: 1.2 + 0.5 + 1.2 + 3 × 0.05 = 3.05 cm.
9. 3.45 cm
Each side's upper limit is 0.05 cm more, three of them 3 × 0.05: 1.1 + 0.8 + 1.4 + 3 × 0.05 = 3.45 cm.

10. False
The total lies in 13 × (47 − 0.5) = 604.5 ≤ W < 13 × (47 + 0.5) = 617.5.
11. D. 61.5 m
Each of the four sides can be out by 0.5 m: the perimeter lies in 58 ≤ P < 62.
12. True
The total lies in 19 × (26 − 0.5) = 484.5 ≤ W < 19 × (26 + 0.5) = 503.5.

Marking: 2 for the working, 1 for the answer, 1 for the sentence.

13. True
The total can be nearly 15 × (58 + 0.5) = 877.5 kg: if that is more than 872, it could be overloaded.
14. 97.3125, 99.3125
The lower limits multiplied: (11.3 − 0.05) × (8.7 − 0.05) = 97.3125; the upper limits: (11.3 + 0.05) × (8.7 + 0.05) = 99.3125.
15. 8 cups
The worst case: the juice at its least, 2.1 L − 0.05 L = 2050 mL, each cup nearly 255 mL; 2050 ÷ 255 has whole part 8.
16. 1200.25 cm³
The volume's upper limit is (20 + 0.5)³ = 8615.125 and its lower limit (20 − 0.5)³ = 7414.875: 1200.25 cm³ apart. The edge is out by under 1 cm, the volume by far more.
17. C. 435.25 g
The total lies in 12 × (36 − 0.5) = 426 ≤ W < 12 × (36 + 0.5) = 438.
18. 30 tiles
The most there can be: the corridor at nearly 8 m + 0.5 m = 850 cm, the tiles at their shortest, 27.5 cm; 850 ÷ 27.5 has whole part 30.

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