Question

metric conversion quiz retake prerequisite
you must fully complete this worksheet following the directions in the questions in order to retake the quiz

1. convert 4.30 x 10³ mg to fg using dimensional analysis. show complete work with units and answer with the correct number of significant figures.

Explanation:

Step1: Recall unit conversions

We know that \(1\space \text{Mg} = 10^{6}\space \text{g}\) and \(1\space \text{g} = 10^{15}\space \text{fg}\). So, first convert Mg to g, then g to fg.
Given \(4.30\times 10^{3}\space \text{Mg}\), convert to g: \(4.30\times 10^{3}\space \text{Mg}\times\frac{10^{6}\space \text{g}}{1\space \text{Mg}}\)

Step2: Convert g to fg

Now take the result from step 1 and convert to fg: \((4.30\times 10^{3}\times 10^{6}\space \text{g})\times\frac{10^{15}\space \text{fg}}{1\space \text{g}}\)
Using exponent rules \(a^{m}\times a^{n}=a^{m + n}\), so \(10^{3}\times10^{6}\times10^{15}=10^{3 + 6+15}=10^{24}\)
And \(4.30\times10^{24}\space \text{fg}\) (since the number of significant figures is determined by the given value \(4.30\times 10^{3}\) which has 3 significant figures)

Answer:

\(4.30\times 10^{24}\space \text{fg}\)