Question

Use dimensional analysis to find the number of cm/min in 5.8 m/hr. Show your work and be sure to calculate the answer in the correct number of significant figures.

Answer 1

dimensional analysis sounds fancy. You just need to know the relationship between the units:
1 m = 100 cm
1 hr = 60 min

You can then divide what ever conversion you want over on the other side, in our case we want to go from meter to centimeter and from hours to minutes:
\[1~\textrm{m}=60~ \textrm{cm} \rightarrow 1=100\frac{ \textrm{cm} }{ \textrm{m} }\]
\[1~\textrm{hr}=60~\textrm{mïn} \rightarrow 1=\frac{1 }{ 60 } \frac{ \textrm{ hr} }{ \textrm{mïn} }\]

You are always allowed to multiply any expression with one as:\[x \times 1=x\]
So we get:
\[\large 5.8~\frac{ \textrm{m} }{ \textrm{hr} } \times 10~\frac{ \textrm{cm} }{ \textrm{m} } \times \frac{ 1 }{ 60 }~\frac{ \textrm{hr} }{ \textrm{mïn} }=\]

Answer 2

For the practice, try see if the units cancel and make sure to write the answer with the right amount of significant numbers.