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The mass, m tonnes, of a girder is 12.7, correct to 1 decimal place - OCR - GCSE Maths - Question 14 - 2017 - Paper 1
Question 14
The mass, m tonnes, of a girder is 12.7, correct to 1 decimal place. Complete the error interval for the mass, m. (b) The length of a piece of wood is given as 8 m... show full transcript
Worked Solution & Example Answer:The mass, m tonnes, of a girder is 12.7, correct to 1 decimal place - OCR - GCSE Maths - Question 14 - 2017 - Paper 1
Step 1
Complete the error interval for the mass, m.
Answer
To find the error interval for the mass given as 12.7 tonnes, you need to consider the effect of rounding to one decimal place:
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The lower limit is calculated by subtracting half of the smallest unit at the decimal place (0.05) from the given value:
Lower limit: tonnes.
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The upper limit is calculated by adding 0.05 to the given value:
Upper limit: tonnes.
Therefore, the error interval for the mass, m, is:
Step 2
Show that the piece of wood could be longer than the metal rod.
Answer
To determine whether the piece of wood could be longer than the metal rod, we assess their lengths:
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The length of the piece of wood is given as 8 metres, correct to the nearest metre. Therefore, the maximum length can be calculated as follows:
Maximum length of wood = metres.
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The length of the metal rod is given as 8.5 metres, correct to one decimal place, which gives us an error range:
- Lower limit for metal rod: metres.
- Upper limit for metal rod: metres.
Now we compare the maximum length of the wood (8.5 metres) with the overlapping range of the metal rod (8.45 to 8.55 metres):
The maximum length of the piece of wood (8.5 metres) is equal to the lower limit of the metal rod but isn’t necessarily longer than the rod. However, for lengths longer than 8.5 metres, we can state that there are lengths of wood up to 8.49 metres, which means the wood could indeed be longer than the metal rod.