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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 me... 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 determine the error interval for the mass of the girder, we first note that it is given as 12.7 tonnes, correct to 1 decimal place.
The lower limit of the error interval can be calculated as follows:
- The value of 12.7 rounded to 1 decimal place means it could be as low as 12.65 tonnes.
The upper limit of the error interval is calculated similarly:
- The value of 12.7 could round to 12.7 but be just below 12.75 tonnes.
Thus, the error interval for m is:
Step 2
Show that the piece of wood could be longer than the metal rod.
Answer
The length of the piece of wood is given as 8 metres, correct to the nearest metre. Therefore, the error interval for the piece of wood can be determined as follows:
- Lower limit = 8 - 0.5 = 7.5 metres
- Upper limit = 8 + 0.5 = 8.5 metres
Hence, the possible lengths for the piece of wood are between 7.5 metres and 8.5 metres, inclusive.
For the metal rod, whose length is given as 8.5 metres, correct to 1 decimal place, the error interval is:
- Lower limit = 8.5 - 0.05 = 8.45 metres
- Upper limit = 8.5 + 0.05 = 8.55 metres
Thus, the length of the metal rod ranges from 8.45 metres to 8.55 metres.
Now, comparing the intervals:
- The maximum length of the piece of wood is 8.5 metres.
- The minimum length of the metal rod is 8.45 metres.
Since the maximum length of the wood piece (8.5 metres) is equal to the maximum length of the metal rod (8.55 metres) but could also be less than that, we find that the piece of wood, when at its maximum length, could match but not exceed the metal rod.
However, there is a portion of the wood's interval (specifically its minimum of 7.5 metres) which has values that are definitely longer than the entire interval of the metal rod. Hence, it’s plausible that the piece of wood could indeed be longer than the metal rod.