Question

complete the following subtraction 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 subtraction

\[

$$\begin{align*} 5.55555\times 10^{5}\ \mu g-5.55\times 10^{5}\ \mu g&=(5.55555 - 5.55)\times10^{5}\ \mu g\\ &= 0.00555\times 10^{5}\ \mu g\\ &=555\ \mu g \end{align*}$$

\]
The second - number $5.55\times 10^{5}\ \mu g$ is precise to the hundredths place in the coefficient part. When subtracting, the result should be reported to the same precision as the least - precise number in the operation.

Step2: Determine the uncertainty

The uncertainty is related to the precision of the least - precise number used in the subtraction. The number $5.55\times 10^{5}\ \mu g$ has an uncertainty of $\pm0.01\times 10^{5}\ \mu g$ (because it is given to two decimal places in the coefficient). Converting $0.01\times 10^{5}\ \mu g$ to standard form gives $1\times 10^{3}\ \mu g$.

Answer:

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