Question

You need a 450 microgram sample of gold, but you only have a mass balance that measures in decigrams. Convert the amount of gold you need to decigrams by comparing the exponents. Provide your answer in scientific notation. Be sure to show your work.

Options:
A) 4.5 x 10^3 dg
B) 4.5 x 10^-3 dg
C) 4.5 x 10^4 dg
D) 4.5 x 10^-4 dg

Answer 1

To convert 450 micrograms to decigrams, you divide 450 micrograms by 1,000,000 to convert to grams and then multiply by 10 to convert to decigrams. The correct conversion is 4.5 x 10^-3 dg.

Step-by-step explanation:

The question requires converting 450 micrograms to decigrams. To begin with, we must understand the relationship between grams and the units micrograms and decigrams. 1 gram equals 1,000,000 micrograms (1g = 106 µg) and 1 gram equals 10 decigrams (1g = 10 dg). Therefore, to convert micrograms to grams, you divide by 1,000,000, and to convert grams to decigrams, you multiply by 10.

To convert 450 micrograms (450 µg) to grams, divide by 1,000,000: 450 µg / 106 = 4.5 x 10-4 g. Now convert this to decigrams by multiplying by 10: 4.5 x 10-4 g × 10 = 4.5 x 10-3 dg.

The correct conversion from 450 micrograms to decigrams is 4.5 x 10-3 dg, which corresponds to option B in the multiple choice selection provided.