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A grain of salt weighs 6.48 x 10^{-5} kg on average - OCR - GCSE Maths - Question 1 - 2019 - Paper 6
Question 1
A grain of salt weighs 6.48 x 10^{-5} kg on average. A packet contains 0.35 kg of salt. (a) Use this information to calculate the number of grains of salt in the pa... show full transcript
Worked Solution & Example Answer:A grain of salt weighs 6.48 x 10^{-5} kg on average - OCR - GCSE Maths - Question 1 - 2019 - Paper 6
Step 1
(a) Use this information to calculate the number of grains of salt in the packet.
Answer
To find the number of grains of salt in the packet, we can use the formula:
ext{Number of grains} = rac{ ext{Total weight of salt in kg}}{ ext{Weight of one grain in kg}}Substituting the values:
- Total weight of salt = 0.35 kg
- Weight of one grain of salt = 6.48 x 10^{-5} kg
The equation becomes:
ext{Number of grains} = rac{0.35}{6.48 imes 10^{-5}}Calculating this, we have:
ext{Number of grains} ext{ } egin{align*} = rac{0.35}{6.48 imes 10^{-5}} \ = 5404.0 ext{ grains} \ ext{(which rounds to either 5404 or 5405)} ext{ }egin{align*}Thus, the number of grains of salt in the packet is approximately 5404.
Step 2
(b) Explain why your answer to part (a) is unlikely to be the actual number of grains of salt in the packet.
Answer
The calculated number of grains of salt (5404) is based on an average weight per grain. In practice, the weight of individual grains can vary due to factors such as moisture content, impurities, and size variation. Therefore, the actual number of grains may differ from the calculated value as the grains might not all have the same weight, leading to discrepancies in total counts. Additionally, as the number of grains must be a whole number, this adds further uncertainty to the final count.