Question

a pound of sugar weighs approximately $4.5 \times 10^{2}$ grams. if each grain of sugar weighs $6.25 \times 10^{-4}$ of a gram, which is the best estimate for the number of grains of sugar in a 5 - pound bag?\
\bigcirc a. $3.6 \times 10^{8}$ grains\
\bigcirc b. $3.6 \times 10^{6}$ grains\
\bigcirc c. $3.6 \times 10^{7}$ grains\
\bigcirc d. $3.6 \times 10^{5}$ grains

Explanation:

Step1: Calculate total grams in 5 lbs

Total grams = $5 \times 4.5 \times 10^2 = 22.5 \times 10^2 = 2.25 \times 10^3$

Step2: Divide by grain weight

Number of grains = $\frac{2.25 \times 10^3}{6.25 \times 10^{-4}}$

Step3: Compute coefficient and exponents

Coefficient: $\frac{2.25}{6.25} = 0.36$
Exponents: $10^{3 - (-4)} = 10^7$

Step4: Adjust to proper scientific notation

$0.36 \times 10^7 = 3.6 \times 10^6$

Answer:

B. $3.6 \times 10^6$ grains