Conversions with dimensional analysis

Question

An object is moving at a speed of 390 centimeters per hour. Express this speed in kilometers per week round your answer to the nearest hundredth.

Answer 1

Unit conversion like this is all about finding conversion factors that lead to the result desired. In this case we need to go from cm to kilometers and from hours to weeks. We might need to d these in more than 1 step, but that's OK. First, lets go from cm to meters. There are 100 cm in 1 meter. Since we are starting from 390 cm/hr, notice that cm is in the numerator (on top). To eliminate cm, we must have the cm to meter conversion with the cm on bottom. That way cm on to cancels with cm on bottom and that unit is eliminated. So we can multiply by 1m/100cm (essentially dividing by 100). Then, we know that there are 1000 meters in 1 kilometer so we can multiply by 1km/1000m (essentially dividing by 1000). Next, there are 24 hours per day so we can multiply by 24 hr/1 day and then again by 7 days/1 week. The result looks like this:

We find the final answer by multiplying 390 by 24 and by 7 then dividing by 100 and 1000 and we get 0.6552 km/wk. Since we are instructed to round the nearest hundredth, the final answer is 0.66 km/wk

Answer 2

Mason

First convert cms to kms

1 km = 1000 m = 1000 x 100cm = 100000 cm

So 1 cm = 1/100000 km

So 360 cm = 360 x (1/100000) km

24 hrs in a day, so 24 x 7 hrs in a week

So in 1 hr, 360 x (1/100000) km

In 1 week, 24 x 7 x 360 x (1/100000) = 0.6048 km

So 0.6048 km / week

Mike