Question

question 3 (1.666666667 points)
complete the following subtraction using significant figures. 5.55555 x 10^5 μg - 5.55 x 10^5 μg =
what is the largest uncertainty in the two numbers? (select two different answers 1 and 2 in the order given in the answers)
a. +/- 0.00001 x 10^5 μg
b. +/- 0.01 μg
c. +/- 0.01 x 10^5 μg
d. +/- 1 x 10^3 μg

Explanation:

Step1: Perform the subtraction

\[

$$\begin{align*} 5.55555\times 10^{5}\ \mu g-5.55\times 10^{5}\ \mu g&=(5.55555 - 5.55)\times 10^{5}\ \mu g\\ &=0.00555\times 10^{5}\ \mu g\\ & = 555\ \mu g \end{align*}$$

\]

Step2: Analyze uncertainties

For the number \(5.55555\times 10^{5}\ \mu g\), the uncertainty is \(\pm0.00001\times 10^{5}\ \mu g\). For the number \(5.55\times 10^{5}\ \mu g\), the uncertainty is \(\pm0.01\times 10^{5}\ \mu g = \pm1\times 10^{3}\ \mu g\). The larger uncertainty is \(\pm0.01\times 10^{5}\ \mu g=\pm 1\times 10^{3}\ \mu g\).

Answer:

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