An analysis showed a sample to contain 0.00471 grams of lead. How many micrograms is this?
A. $0.471 \mu g$
B. $4.71 \times 10^3 \mu g$
C. $4.71 \times 10^6 \mu g$
D. $4.71 \times 10^{-2} \mu g$
E. $4.71 \times 10^{-6} \mu g$
Answer (1)
We are given a mass in grams and need to convert it to micrograms.
Recall the conversion factor: 1 g = 1 0 6 μg .
Multiply the given mass by the conversion factor: 0.00471 × 1 0 6 = 4710 .
Express the answer in scientific notation: 4.71 × 1 0 3 μg .
Explanation
Understanding the Problem We are given a mass of lead in grams and asked to convert it to micrograms. To do this, we need to know the conversion factor between grams and micrograms.
Stating the Conversion Factor We know that 1 gram (g) is equal to 1,000,000 micrograms ( μg ). This can be written as: 1 g = 1 0 6 μg
Applying the Conversion To convert 0.00471 grams to micrograms, we multiply 0.00471 by the conversion factor 1 0 6 :
0.00471 g × 1 0 6 g μg = 0.00471 × 1 0 6 μg
Calculating the Result Now, we perform the multiplication: 0.00471 × 1 0 6 = 4710
Final Answer Therefore, 0.00471 grams is equal to 4710 micrograms. We can also express this in scientific notation as 4.71 × 1 0 3 μg .
Examples
Imagine you're measuring a tiny amount of medicine using a very precise scale. The scale reads the mass in grams, but the prescription requires the mass in micrograms because micrograms are much smaller units. Converting grams to micrograms is essential to ensure the correct dosage is administered. This conversion is also useful in chemistry when dealing with very small quantities of substances in experiments, ensuring accurate measurements and results.
