To estimate the number of grains of sugar in a 5-pound bag, we first need to find out how many grams of sugar are in a 5-pound bag.
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Convert pounds to grams: \[ 5 \text{ pounds} = 5 \times 4.5 \times 10^2 \text{ grams} \] \[ = 22.5 \times 10^2 \text{ grams} \] \[ = 2.25 \times 10^3 \text{ grams} \]
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Calculate the number of grains of sugar per gram: Each gram of sugar weighs \(6.25 \times 10^{-4}\) grams, so the number of grains in one gram is the reciprocal of this value: \[ \text{Number of grains in 1 gram} = \frac{1 \text{ gram}}{6.25 \times 10^{-4} \text{ grams/grain}} = \frac{1}{6.25 \times 10^{-4}} \] Simplifying this gives us: \[ = 1.6 \times 10^3 \text{ grains} \quad \text{(since } \frac{1}{6.25} = 0.16 \text{ and } \frac{1}{10^{-4}} = 10^4\text{)} \]
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Calculate the total number of grains in 2.25 \times 10^3 grams: Now, to find the total number of grains in a 5-pound bag: \[ \text{Total grains} = 2.25 \times 10^3 \text{ grams} \times 1.6 \times 10^3 \text{ grains/gram} \] \[ = 3.6 \times 10^6 \text{ grains} \]
Thus, the best estimate for the number of grains of sugar in a 5-pound bag is approximately \( \boxed{3.6 \times 10^6} \) grains.