29
0.7kg
/
×
10
3
g
1kg
/
=700g.
To convert grams to kilograms, you would simply flip the fraction upside
down.
One advantage of this method is that it can easily be applied to a series
of conversions. For instance, to convert one year to units of seconds,
1year
/
×
365days
/
1year
/
×
24hours
/
1day
/
×
60min
/
1hour
/
×
60s
1min
/
= 3.15 x 10
7
s.
Should that exponent be positive or negative.
A common mistake is to write the conversion fraction incorrectly. For
instance the fraction
10
3
kg
1g
(incorrect)
does not equal one, because 10
3
kg is the mass of a car, and 1 g is the mass
of a raisin. One correct way of setting up the conversion factor would be
10
–3
kg
1g
.(correct)
You can usually detect such a mistake if you take the time to check your
answer and see if it is reasonable.
If common sense doesn’t rule out either a positive or a negative expo-
nent, here’s another way to make sure you get it right. There are big prefixes
and small prefixes:
big prefixes:kM
small prefixes:m
µ
n
(It’s not hard to keep straight which are which, since “mega” and “micro” are
evocative, and it’s easy to remember that a kilometer is bigger than a meter
and a millimeter is smaller.) In the example above, we want the top of the
fraction to be the same as the bottom. Since k is a big prefix, we need to
compensate by putting a small number like 10
-3
in front of it, not a big
number like 10
3
.
Discussion Question
Each of the following conversions contains an error. In each case, explain
what the error is.
(a) 1000 kg x
1
k
g
1000g
= 1 g(b) 50 m x
1cm
100m
= 0.5 cm
(c) "Nano" is 10
-9
, so there are 10
-9
nm in a meter.
(d) "Micro" is 10
-6
, so 1 kg is 10
6
µ
g.
Section 0.9Conversions