GCSE OCR Maths Decimals: A grain of salt weighs 6.48 x 10

A grain of salt weighs 6.48 x 10^{-5} kg on average - OCR - GCSE Maths - Question 1 - 2019 - Paper 6

Question 1

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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

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 start with the total weight of salt in kilograms, which is given as 0.35 kg.

First, we convert this weight into grams because calculating the number of grains makes more sense in smaller weights. Since 1 kg = 1000 grams:

0.35 ext{ kg} = 0.35 imes 1000 = 350 ext{ g}

Next, we convert grams into kilograms for consistency in units:

Since each grain of salt weighs 6.48 x 10^{-5} kg, we can determine the number of grains by dividing the total weight of salt in kg by the weight of one grain:

ext{Number of grains} = \frac{0.35 ext{ kg}}{6.48 imes 10^{-5} ext{ kg/grain}}\

Calculating this yields:

ext{Number of grains} = \frac{0.35}{6.48 \times 10^{-5}} = 5403.58 ext{ grains} \approx 5404 ext{ grains}

Thus, the answer is approximately 5404 grains.

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 answer of approximately 5404 grains is unlikely to be the exact number of grains for several reasons:

Average Weight: The weight of a grain of salt is an average value. In reality, grains may weigh slightly more or less than 6.48 x 10^{-5} kg, leading to variations in the actual count.
Grains are Discrete: The number of grains must be an integer since you cannot have a fraction of a grain. The calculated result suggests the presence of a fractional grain, indicating that the exact number might be rounded.
Measurement Errors: There may have been errors in measuring the total weight of salt or the weight of an individual grain, which could lead to discrepancies in the final count.

Due to these factors, while the calculation provides an estimate, the actual number of grains is likely to be slightly different.

A grain of salt weighs 6.48 x 10^{-5} kg on average - OCR - GCSE Maths - Question 1 - 2019 - Paper 6

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

Calculate the number of grains of salt in the packet.

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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