Question

ne juice bottle of fruit juice contains total of 488 mg of phosphorus, rounded to the nearest milligram (mg). juice contains a total of 1.62 litres of juice, rounded to 2 d.p. The bo M the lower bound of the mass of phosphorus, in milligrams (mg), that there could be in 1 litre of the fruit juice.​

Answer 1

To calculate the lower bound of phosphorus per liter of juice, divide the possible minimum phosphorus content (487.5 mg) by the maximum possible volume of juice (1.625 liters).

Step-by-step explanation:

To find the lower bound of the mass of phosphorus per liter in the fruit juice, we consider the worst-case scenario for both the amount of phosphorus and the volume of juice due to rounding. Since the phosphorus content is rounded to the nearest milligram, the actual amount could be slightly less than 488 mg – as low as 487.5 mg. Likewise, the volume of juice is 1.62 liters, rounded to two decimal places, so the actual volume could be slightly more than this – up to 1.625 liters (since the next hundredth would round up to 1.63 liters).

Calculating the lower bound, we'd use the possible minimum amount of phosphorus and the maximum volume of juice:

• Lower bound of phosphorus per liter = (487.5 mg) / (1.625 liters)

Perform this calculation to find the lower bound in mg/L.

Answer 2

To find the lower bound of the mass of phosphorus in 1 liter of the fruit juice, we need to assume that all of the phosphorus is concentrated in just one liter of the juice. Therefore, the lower bound will be the mass of phosphorus in the entire bottle divided by the total volume of the bottle, which is 1.62 liters.

The mass of phosphorus per liter of juice is given by:

488 mg ÷ 1.62 L ≈ 301.2 mg/L

Rounding this to the nearest milligram, we get:

301 mg/L

Therefore, the lower bound of the mass of phosphorus in 1 liter of the fruit juice is approximately 301 mg.