1-2 Unit Conversions, And Significant Figures
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1
2Answer to Essential Question 1.1: A model is simplified version of physical situation. Using a
model enables us to focus on the key elements of a particular situation, and is one way of getting
a good idea of what is going on without having to consider every fine detail.
1-2 Unit Conversions, and Significant Figures
It is often necessary to convert a value from one set of units to another. To do this, we
need to know the appropriate conversion factors. For instance, in Example 1.2 we will make use
of these conversion factors:
•
1 hour = 3600 seconds
•
1 km = 1000 m
•
1 mile = 1.609344 km
EXAMPLE 1.2 – Unit conversions
At the 2009 World Championships in Athletics, held in Berlin, the Jamaican sprinter
Usain Bolt set a world record for the 200-meter dash by running that distance in a time of 19.19 s.
Assuming he ran exactly 200 m in this time, what was Usain Bolt’s average speed during the race
in
(a) m/s; (b) km/h; (c) miles per hour?
SOLUTION
(a) The first thing we need to do is to understand what an average speed is. Average speed
is the total distance covered divided by the time in which it was covered. If we divide the given
distance by the given time we’ll get the answer we’re looking for:
200 m
= 10.422094841063 m/s
Usain Bolt’s average speed was:
19.19 s
This brings up the idea of significant figures, because you certainly do not want to quote
an answer with 14 significant figures, as is shown above. Instead, round off the answer to four
significant figures, because there are four in the time of 19.19 s. The rule is, when you multiply
or divide numbers you look at the number of significant figures in the values going into the
calculation and round off to the smallest number of significant figures. Here, we’re saying that
the distance of 200 m is exact (see the assumption stated in the example), so that number has an
infinite number of significant figures, while the time has four significant figures.
It would be more realistic to make the following argument. Lengths on a track,
particularly at a major international competition such as the World Championships, are measured
very accurately. For argument’s sake, let’s say the 200 meter distance is accurate to within 1
centimeter. Thus, the distance Usain Bolt ran was 200.00 m, seeing as 1 cm = 0.01 m. There are
five significant figures in 200.00, so when dividing a number with five significant figures by one
with four, we should round off our final answer to four significant figures.
Thus, Usain Bolt’s average speed was 10.42 m/s.
(b) To convert from m/s to km/h, we need to know that there are 1000 m in 1 km, and that
there are 3600 s in 1 hour. Then, we simply set these conversion factors up as ratios so that the
units cancel properly, as follows:
m
1 km
3600 s
!
!
= 37.52 km/h .
10.4221
s
1000 m
1 h
Chapter 1 – Introduction to Physics
Page 1 – 4
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