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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

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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

Use this information to calculate the number of grains of salt in the packet.

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Answer

To find the number of grains of salt in the packet, we can use the formula:

N=WwN = \frac{W}{w}

where:

  • NN = number of grains of salt,
  • WW = total weight of salt in the packet,
  • ww = weight of one grain of salt.

Substituting the values:

W=0.35kg=0.35×103g=350gW = 0.35 kg = 0.35 \times 10^{3} g = 350 g

w=6.48×105kg=6.48×102gw = 6.48 \times 10^{-5} kg = 6.48 \times 10^{-2} g

Now, we can plug in these values:

N=3506.48×1025402.48N = \frac{350}{6.48 \times 10^{-2}} \approx 5402.48

Therefore, rounding to the nearest whole number, the number of grains of salt is approximately 5402.

Step 2

Explain why your answer to part (a) is unlikely to be the actual number of grains of salt in the packet.

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Answer

The calculated number of grains of salt in the packet is based on average values for the weight of each grain. In reality, grains of salt can vary in size and weight due to factors like impurities and crystal structure. As a result, the actual number of grains could be more or less than the calculated value. Furthermore, since the number of grains must be an integer, any fractional part in the result indicates that the exact count isn't an attainable value.

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