Question

1. complete the following calculation using correct significant figures: (27.3) x (120) x (2.722 x 10²) ÷ (3.20 x 10⁻⁵) =

Explanation:

Step1: Perform the multiplication and division

$$\begin{align*} &\frac{27.3\times120\times2.722\times 10^{2}}{3.20\times 10^{-5}}\\ =&\frac{27.3\times120\times272.2}{3.20\times 10^{-5}}\\ =&\frac{27.3\times120\times272.2}{3.20}\times10^{5} \end{align*}$$

First, calculate \(27.3\times120 = 3276\), then \(3276\times272.2=3276\times(270 + 2.2)=3276\times270+3276\times2.2=884520+7207.2 = 891727.2\)

Then \(\frac{891727.2}{3.20}=278664.75\)

So \(\frac{27.3\times120\times272.2}{3.20}\times10^{5}=278664.75\times10^{5}\)

Step2: Consider significant figures

• \(27.3\) has 3 significant figures.
• \(120\) has 2 significant figures.
• \(2.722\times10^{2}\) has 4 significant figures.
• \(3.20\times10^{-5}\) has 3 significant figures.

The number with the least number of significant figures in the multiplication/division is \(120\) (2 significant figures).

So \(278664.75\times10^{5}\approx2.8\times 10^{10}\)

Answer:

\(2.8\times 10^{10}\)