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A pound of sugar weighs approximately [tex]4.5 \times 10^2[/tex] grams. If each grain of sugar weighs [tex]6.25 \times 10^{-4}[/tex] of a gram, which is the best estimate for the number of grains of sugar in a 5-pound bag?

A. [tex]3.6 \times 10^8[/tex] grains
B. [tex]3.6 \times 10^6[/tex] grains
C. [tex]3.6 \times 10^7[/tex] grains
D. [tex]3.6 \times 10^5[/tex] grains

Answer :

The best estimate for the number of grains of sugar in a 5-pound bag is approximately 3.6 × 10^7 grains (option C).

To find the best estimate for the number of grains of sugar in a 5-pound bag, we need to determine the number of grains in 1 pound and then multiply it by 5.

The weight of 1 pound of sugar is given as 4.5 × 10^2 grams. To find the number of grains in 1 pound, we divide the weight of 1 pound by the weight of each grain, which is 6.25 × 10^(-4) grams.

Number of grains in 1 pound = (4.5 × 10^2 grams) / (6.25 × 10^(-4) grams)

Simplifying the expression, we get:

Number of grains in 1 pound = (4.5 × 10^2) / (6.25 × 10^(-4)) = (4.5 × 10^2) × (10^4 / 6.25)

Number of grains in 1 pound ≈ 7.2 × 10^6 grains

Finally, we multiply the number of grains in 1 pound by 5 to find the best estimate for the number of grains in a 5-pound bag:

Best estimate for the number of grains in a 5-pound bag ≈ (7.2 × 10^6 grains) × 5 = 3.6 × 10^7 grains

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