Game Development Reference
In-Depth Information
In this situation, to represent the rational number in scientific notation, you
begin by converting the denominator to a power of ten.
n
2
1000
¼
5
:
2
10
3
¼
5
5
:
2
10
3
:
You then use a negative exponent to convert the number into scientific
notation.
n
Here are a couple of examples of converting back and forth. In the first
example, you shift the decimal point to the right two places to reflect the
exponent of 10. In the lower example, you begin with an integer value. To
make it clearer how to convert the number from scientific notation to a
rational number, you can convert the integer to a rational number, and then
shift the decimal point three digits to the left.
908
10
2
2
:
¼
290
:
8
4
10
3
0
10
3
¼
4
:
¼ :
004
If you can find ways to reduce the complexity of fractions, then it becomes
easier to deal with scientific notation. In this case, you begin with a numerator
that requires you to multiply two numbers given in scientific notation.
n
2
10
5
ð
4
10
3
8
10
2
8
10
7
¼
1
10
2
Þ
10
7
¼
10
2
ð
7
Þ
¼
10
2
þ
7
¼
10
9
¼
8
10
7
You multiply 2 by 4 to arrive at 8 in the numerator. When you rewrite the
expression so that 8/8 equals 1, then you are in a position to work with only
the exponents of 10. To carry out the division, you subtract the negative
exponent of the denominator from the positive exponent of the numerator,
resulting in 10 to the power of 9.
Exercise Set 3.2
Solve the following problems. Express the answer in scientific notation.
45 10
6
0765 10
3
a.
ð3
:
Þð5
:
Þ
43 10
3
2
b.
ð5
:
Þ
56 10
3
c.
2
:
45 10
4
d. From Table 3.2, what is the ratio of the age of the solar system to the age of the universe?
3
:
