Errors in measurement · Ages 13–14
Errors in measurement at work
Most pieces = upper ÷ lower; area: lower × lower to upper × upper.
How to do it
Method
Most pieces = upper ÷ lower; area: lower × lower to upper × upper
10 bags of 5 kg: 45 ≤ total < 55
Another way
Check with the measured values
10 × 5 = 50, between 45 and 55
In full
Putting several measurements together, each could be high or low, so take each one's upper or lower limit as needed. A total: the lower limits added ≤ the true total < the upper limits added. Ten bags of rice, each 5 kg to the nearest 1 kg, weigh at least 10 × 4.5 = 45 kg and less than 10 × 5.5 = 55 kg. The most pieces a rope can be cut into: the longest rope and the shortest pieces, so the rope's upper limit ÷ a piece's lower limit, the decimals dropped. The fewest pieces you are sure of: the rope's lower limit ÷ a piece's upper limit, dropped the same way. A rectangle's area: least = the two lower limits multiplied, greatest = the two upper limits multiplied (the true area is less than it). Check: the measured values put in give a result inside the range.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
13 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
Show the answer and working
Answer: 370.5, 383.5
Each bag is from 28.5 kg up to 29.5 kg: at least 13 × 28.5 = 370.5, less than 13 × 29.5 = 383.5.
Example 2
A roll of wire is 42 m long, to the nearest 1 m; each piece is 6 m (to the nearest 1 m). Whatever the true lengths, how many pieces can always be cut, at least?
Show the answer and working
Answer: 6 pieces
The worst case: the wire at its shortest, 41.5 m, each piece nearly 6.5 m: 41.5 ÷ 6.5 is just over 6, so 6 pieces for sure.
Example 3
10 books each weigh 11 g to the nearest 1 g. Their total weight could be 115 g.
True or false?
Show the answer and working
Answer: False
The total lies in 10 × (11 − 0.5) = 105 ≤ W < 10 × (11 + 0.5) = 115.
Practice questions to try
Try these 5; the answers are at the end. For a whole worksheet, see VIP worksheets below.
1.A roll of ribbon is 63 m long, to the nearest 1 m. Each piece is to be 4 m long (to the nearest 1 m). At most how many pieces can be cut?
Answer:
2.17 bags of rice each weigh 22 kg to the nearest 1 kg. Their total weight W lies in kg ≤ W < kg.
Fill in each blank
Answer:
3.A roll of wire is 77 m long, to the nearest 1 m; each piece is 2 m (to the nearest 1 m). Whatever the true lengths, how many pieces can always be cut, at least?
Answer:
4.19 books each weigh 15 g to the nearest 1 g. Their total weight could be 295.5 g.
True or false?
Answer:
5.A square tile's side is measured as 14 cm to the nearest 1 cm, so its area works out as 196 cm². By how many cm² is the area's upper limit more than 196 cm²?
Answer:
All the answers
- 1. 18 pieces
- 2. 365.5, 382.5
- 3. 30 pieces
- 4. False
- 5. 14.25 cm²
VIP practice notes and papers
Aimed at tests and exams: questions on this topic, new every time, to print or save as a PDF.
- Practice notes: The key point, worked examples step by step, then questions of the same kind to follow, hints fading
- Practice paper: Set out in parts like a school paper, marked, with answers and full working
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