A pound of sugar weighs approximately 4.5 × 102 grams. If each grain of sugar weighs 6.25 × 10-4 of a gram, which is the best estimate for the number of grains of sugar in a 5-pound bag?
A.
3.6 × 107 grains
B.
3.6 × 108 grains
C.
3.6 × 106 grains
D.
3.6 × 105 grains
B. 3.6 × 108 grains
To find the number of grains in a 5-pound bag of sugar, first convert the weight of a pound of sugar to grams:
1 pound = 4.5 × 10^2 grams
Then multiply this by 5 to find the weight of a 5-pound bag in grams:
5 pounds = 5 * 4.5 × 10^2 = 22.5 × 10^2 = 2.25 × 10^3 grams
Now, divide the weight of the bag in grams by the weight of each grain of sugar to find the number of grains:
2.25 × 10^3 / 6.25 × 10^-4 = 2.25 * 10^3 / 6.25 * 10^-4 = 2.25 / 6.25 * 10^(3+4) = 0.36 * 10^7 = 3.6 * 10^8 grains
Therefore, the best estimate for the number of grains of sugar in a 5-pound bag is 3.6 × 10^8 grains.
are you sure
My previous response contains a mistake in the calculation. Let's correct it:
1 pound = 4.5 x 10^2 grams
5 pounds = 5 x 4.5 x 10^2 = 22.5 x 10^2 = 2.25 x 10^3 grams
Now, divide the weight of the bag in grams by the weight of each grain of sugar to find the number of grains:
2.25 x 10^3 / 6.25 x 10^-4 = (2.25 / 6.25) x 10^(3+4) = 0.36 x 10^7 = 3.6 x 10^6 grains
Therefore, the best estimate for the number of grains of sugar in a 5-pound bag is 3.6 x 10^6 grains.
The correct answer is C. 3.6 x 10^6 grains. Thank you for prompting the double-check.