Measures and solids · Ages 13–14

Upper and lower limits 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 bucket's capacity is measured as 6.7 L to the nearest 0.1 L. The true capacity x lies in ≤ x < .
Fill in each blank
Answer:
2.A bamboo pole is measured as 119 cm to the nearest 1 cm. What is the lower limit of its length, in cm?
Answer:
3.A bag of flour is weighed as 8.5 kg to the nearest 0.5 kg. What is the upper limit of its weight, in kg?
Answer:
4.A bamboo pole is measured as 93 cm to the nearest 1 cm. What is the lower limit of its length, in cm?
Answer:
5.A bag of flour is weighed as 420 kg to the nearest 10 kg. What is the upper limit of its weight, in kg?
Answer:
6.A distance was measured to some unit, and its true value x lies in 8.25 km ≤ x < 8.35 km. What was the distance measured, in km?
Answer:
7.A distance was measured to some unit, and its true value x lies in 575 km ≤ x < 585 km. What was the distance measured, in km?
Answer:
8.A measurement correct to 3 significant figures is 80.8 m. What is its lower limit, in m?
Answer:
9.A measurement has a lower limit of 31 mL and an upper limit of 33 mL. To the nearest how many mL was it measured?
Answer:
10.A measurement has a lower limit of 6.45 mL and an upper limit of 6.55 mL. To the nearest how many mL was it measured?
Answer:

11.A carton's width is measured as 15 cm to the nearest 1 cm. Which of these could be its true width?
- A. 15.5 cm
- B. 14.4 cm
- C. 15.6 cm
- D. 14.5 cm
Choose the right answer
Answer:
12.A watermelon is weighed as 2.2 kg to the nearest 0.1 kg. Its true weight could be 2.125 kg.
True or false?
Answer:

13.A measuring jug can only be read correct to some unit. The reading's upper limit is 142.5 mL and its lower limit 137.5 mL. The reading was mL, to the nearest mL.
Fill in each blank
Working:
Answer:
14.Ming runs 100 m in 17.5 seconds, to the nearest 0.1 second. The true time t lies in s ≤ t < s.
Fill in each blank
Working:
Answer:
15.Ming measures a twig with a ruler as 8 cm to the nearest 1 cm; Ka-yan measures it again as 7.4 cm to the nearest 0.1 cm. Both measurements could be right.
True or false?
Working:
Answer:
16.A newspaper says 7,900 people came to a concert, to the nearest hundred. At most how many people came?
Working:
Answer:
17.A suitcase on a scale shows 48.5 kg (to the nearest 0.1 kg). What is the least it could weigh, in kg?
Working:
Answer:
18.Tsz-hin's height is 164 cm to the nearest 1 cm. Which of these gives Tsz-hin's true height x correctly?
- A. 163.5 ≤ x ≤ 164.5
- B. 163.5 ≤ x < 164.5
- C. 163 ≤ x < 165
- D. 163.5 < x ≤ 164.5
Choose the right answer
Working:
Answer:

Show the answers and working

Upper and lower limits worksheet: Answers and working

1. 6.65, 6.75
Half the unit is 0.05 L: 6.7 − 0.05 = 6.65 and 6.7 + 0.05 = 6.75; the upper limit itself would round up, so it is "<".
2. 118.5 cm
The unit is 1 cm, half of it 0.5 cm: lower limit = 119 − 0.5 = 118.5 cm.
3. 8.75 kg
The unit is 0.5 kg, half of it 0.25 kg: upper limit = 8.5 + 0.25 = 8.75 kg.
4. 92.5 cm
The unit is 1 cm, half of it 0.5 cm: lower limit = 93 − 0.5 = 92.5 cm.
5. 425 kg
The unit is 10 kg, half of it 5 kg: upper limit = 420 + 5 = 425 kg.
6. 8.3 km
The measured value sits halfway between the limits: (8.25 + 8.35) ÷ 2 = 8.3 km.
7. 580 km
The measured value sits halfway between the limits: (575 + 585) ÷ 2 = 580 km.
8. 80.75 m
The third significant figure of 80.8 is in the 0.1 place, so the unit is 0.1 m and half of it 0.05: 80.8 − 0.05 = 80.75 m.
9. 2 mL
The limits are one unit apart: 33 − 31 = 2 mL.
10. 0.1 mL
The limits are one unit apart: 6.55 − 6.45 = 0.1 mL.

11. D. 14.5 cm
The true width lies in 14.5 ≤ x < 15.5: the lower limit 14.5 rounds to 15, so it can be; the upper limit 15.5 rounds up, so it can't.
12. False
The true weight lies in 2.15 ≤ x < 2.25: the lower limit is in, the upper limit is not.

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

13. 140, 5
The reading is halfway between the limits: (137.5 + 142.5) ÷ 2 = 140; the limits are one unit apart: 142.5 − 137.5 = 5.
14. 17.45, 17.55
The unit is 0.1 s, half of it 0.05: 17.5 − 0.05 = 17.45 and 17.5 + 0.05 = 17.55.
15. False
Ming's range is 7.5 ≤ x < 8.5, Ka-yan's 7.35 ≤ x < 7.45; both can be right only if the ranges overlap.
16. 7,949 people
People come in whole numbers: the most that rounds to 7,900 is 7,949 (one more would round to the next hundred). The upper limit 7,900 + 50 itself can't be reached.
17. 48.45 kg
The least is the lower limit: 48.5 − 0.1 ÷ 2 = 48.45 kg.
18. B. 163.5 ≤ x < 164.5
Lower limit 164 − 0.5 = 163.5 (in), upper limit 164 + 0.5 = 164.5 (not in): 163.5 ≤ x < 164.5.

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