Physics for Scientists & Engineers & Modern Physics, 9th Ed

 

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10
chapter 
1
physics and Measurement
1.5 
Estimates and Order-of-Magnitude Calculations
Suppose someone asks you the number of bits of data on a typical musical com-
pact disc. In response, it is not generally expected that you would provide the exact 
number but rather an estimate, which may be expressed in scientific notation. The 
estimate may be made even more approximate by expressing it as an order of magni-
tude, which is a power of ten determined as follows:
 1. 
Express the number in scientific notation, with the multiplier of the power 
of ten between 1 and 10 and a unit.
 2. 
If the multiplier is less than 3.162 (the square root of 10), the order of mag-
nitude of the number is the power of 10 in the scientific notation. If the 
multiplier is greater than 3.162, the order of magnitude is one larger than 
the power of 10 in the scientific notation.
We use the symbol 
, for “is on the order of.” Use the procedure above to verify 
the orders of magnitude for the following lengths:
0.008 6 m 
, 10
2
2
m 0.002 1 m 
, 10
2
3
m 720 m 
, 10
3
m
 
Q 
uick Quiz 
1.3
The distance between two cities is 100 mi. What is the number
of kilometers between the two cities? (a) smaller than 100 (b) larger than 100
(c) equal to 100
Convert meters in the speed to miles:
138.0 m/s2 a
1 mi
1 609 mb
5
2.36 3 10
2
2
mi/s
Convert seconds to hours:
12.36 3 10
2
2
mi/s 
2 a
60 s
1 min
b a
60 min
1 h
b 5 85.0 mi/h
The driver is indeed exceeding the speed limit and should slow down.
What if the driver were from outside the United States and is 
familiar with speeds measured in kilometers per hour? What is the speed of 
the car in km/h?
Answer 
We can convert our final answer to the appropriate units:
185.0 mi/h2 a
1.609 km
1 mi
b 5 137 km/h
Figure 1.3 shows an automobile speedometer displaying speeds in both 
mi/h and km/h. Can you check the conversion we just performed using this 
photograph?