Question

complete the following addition using significant figures. 5.55555×10^5 μg + 5.55×10^5 μg =
what is the uncertainty in the final answer? (select two different answers 1 and 2 in the order given in the answers)
a. +/- 0.00001×10^5 μg
b. +/- 0.01 μg
c. +/- 0.01×10^5 μg
d. +/- 1×10^3 μg

Explanation:

Step1: Perform the addition

\[5.55555\times 10^{5}\ \mu g+5.55\times 10^{5}\ \mu g=(5.55555 + 5.55)\times 10^{5}\ \mu g=11.10555\times 10^{5}\ \mu g\]

Step2: Round to significant - figures

The number \(5.55\times 10^{5}\) has three significant figures. Rounding \(11.10555\times 10^{5}\) to three significant figures gives \(11.1\times 10^{5}\ \mu g = 1.11\times 10^{6}\ \mu g\). The uncertainty is determined by the least - precise measurement. The least - precise measurement is \(5.55\times 10^{5}\ \mu g\), and the uncertainty in \(5.55\times 10^{5}\ \mu g\) is \(\pm0.01\times 10^{5}\ \mu g\) or \(\pm 1\times 10^{3}\ \mu g\)

Answer:

C. \(\pm0.01\times 10^{5}\ \mu g\)
D. \(\pm1\times 10^{3}\ \mu g\)