Use dimensional analysis to convert 75 meters per second to kilometers per hour.

Step-by-step solution

1. 1

   Identify the two exact conversion factors.

   $1\ \text{km}=1000\ \text{m},\qquad 1\ \text{h}=3600\ \text{s}.$

   Both are exact, so the final answer will carry no rounding error at all.

2. 2

   Orient each factor so the unwanted unit cancels. Metres must leave the numerator and seconds must leave the denominator:

   $75\ \frac{\cancel{\text{m}}}{\cancel{\text{s}}}\times\frac{1\ \text{km}}{1000\ \cancel{\text{m}}}\times\frac{3600\ \cancel{\text{s}}}{1\ \text{h}}.$

3. 3

   Combine the two numerical factors into one.

   $\frac{3600}{1000}=3.6,$

   so converting m/s to km/h is always just multiplication by $3.6$ — worth memorising, and it also explains why km/h values are always the larger number.

4. 4

   Multiply.

   $75\times 3.6=270\ \frac{\text{km}}{\text{h}}.$

5. 5

   Check by reversing. Going back, $270\ \text{km/h}\div 3.6=75\ \text{m/s}$, and directly: $270\ \text{km}=270000\ \text{m}$ covered in $3600$ s gives $270000/3600=75$ m/s ✓.