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Order of Magnitude - Questions

Question 1
17552

The volume of a \(5\) litre container is reduced by 2 orders of magnitude. The new volume is?

\(50~\text{ml}\)

\(5 \mathrm{~l}=5000 \mathrm{~ml} \rightarrow 5000 \div 10^{2}=50 \mathrm{~ml}\)

Question 2
17555

By how many orders of magnitude does \({\rm{1}}{\rm{.25 x 1}}{{\rm{0}}^5}~\text{mm}\) differ from \(1.25\,{\rm{x 1}}{{\rm{0}}^{ - 2}}~\text{m}\) ?

\(4\)

\begin{aligned}
1.25 \times 10^{5} \div 1.25 \times 10^{-2} \times 10^{3}&=\frac{1.25 \times 10^{5}}{1.25 \times 10}=10^{4}\\
&\therefore 4
\end{aligned}

Question 3
17558

Water is considered neutral and has a pH of \({\rm{7}}\). If soapy water is \({\rm{100000}}\) times more alkaline, then its pH is?

\(pH = 12\)

\begin{align}
&\text { water } \rightarrow 10^{7} \\
&\begin{aligned}
\text { soapy water } \rightarrow 10^{7} \times 100000=10^{7} \times 10^{5}=10^{12}& \\
\therefore P H=12&
\end{aligned}
\end{align}

Question 4
17562

The largest ever recorded earthquake was in chile in \(1960\) with a magnitude of \({\rm{9}}{\rm{.5}}\) on the Richter scale. The Java earthquake in \(2009\) recorded \({\rm{7}}{\rm{.0}}\). What is the difference in real terms between these two earthquakes?

\(316\;{\rm{x}}\) greater

\begin{aligned}
&\text { Chile }=10^{9.5}, \text { Java }=10^{7} \\
&\text { Difference }=10^{9.5} \div 10^{7}=10^{2.5} \approx 316 \text { times greater. }
\end{aligned}

Question 5
17567

The diameter of the Sun is \({\rm{1}}{\rm{.4\times1}}{{\rm{0}}^6}~\text{km}\). The diameter of the Earth is \({\rm{1}}{\rm{.2\times1}}{{\rm{0}}^4}~\text{km}\) How much greater in magnitude is the Sun's diameter compared to the Earth's?

\(117\;{\rm{x}}\) greater 

\(1.4 \times 10^{6} \div 1.2 \times 10^{4}=117 \times \text { greater. }\)