Game Development Reference
In-Depth Information
Very small numbers, such as Planck's Constant, are represented with a negative
exponent, and the effect is to shift the decimal point 34 places to the left.
Represented literally, 6
626
10
34
becomes
:
0000000000000000000000000000000006626
Carrying out calculations using scientific notation involves performing the usual
mathematical operations with the coefficients, and then using the practices that
pertain to exponents to deal with the powers of 10. Consider, for example, the
problem of how far light travels in a year. If you begin with the speed of light as
shown in Table 3.2, it is 1
0
:
86
10
5
. On the other hand, there are (generally
speaking) 365 days per year. To calculate the number of seconds in a year, you
can use the relationship of days to hours, hours to minutes, and minutes to
seconds: 365
24
60
60
¼
31, 536, 000 seconds per year.
:
1536
10
7
seconds. To calculate the distance
light travels in years you can set up the following expression:
ð
1
Expressed scientifically, you have 3
:
86
10
5
1536
10
7
:
Þð
3
:
Þ¼
1536
Þ
10
5
þ
7
865696
10
12
miles per year
ð
1
:
86
3
:
¼
5
:
A Few Worked Problems
Here are a few worked problems that involve various uses of scientific notation.
n
This problem calls for you to convert a number in scientific notation to
an integer value.
3
10
4
6
:
¼
6
:
3
10,000
¼
63,000
To convert a number from its scientific form to an integer, you begin with
the rational form of the number, and then multiply it by a number consisting
of 1 and a number of zeros corresponding to the number of the exponent
of 10.
n
When you deal with values that are a fraction of 1, you can determine
how to shift the number by converting the exponential form of 10 into a
fraction.
:
:
3
10
2
¼
6
3
100
¼
6
6
1
100
¼
0
3
10
2
6
:
¼
:
3
:
063
10 raised to the power of 2 is 100, and when you multiply 6.3 by 1/100, you
shift the decimal point two digits to the left.
