Game Development Reference
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Convert these numbers to scientific notation.
e. 73,400
f. 0.04764
g. 0.000000000000000000002
h. 1,354,050,000,000,000
Answer the following questions.
i. Without performing actual computations, explain why 4 10 14
is smaller than 3 10 14 .
j. Why is scientific notation so useful?
Absolute Values
Consider what happens when you provide someone with directions to a given
destination. You might receive instructions that indicate distances without
necessarily providing you with the direction in which you are traveling. Con-
sider, for example, an instruction that reads,
''After you turn onto Highway 36, proceed 7 miles.''
Given this instruction, Figure 3.2 illustrates two scenarios. Starting at a given
point, you can then proceed in one of two directions. The distance you travel
involves real movement regardless of whether it takes you nearer to or farther
from your destination. The distance you travel, then, has an absolute value.
Absolute value is the value of a number without respect to whether it is positive
or negative. A number line provides a convenient way to illustrate an absolute
value. Figure 3.3 illustrates a number line. You can use a number line to represent
the arrows depicted in Figure 3.2 in numerical terms. Given this vision, the
number line translates the absolute values of the two directions Figure 3.2
depicts. The number line depicts the distances from 0 to 7 and from 0 to 7. In
both cases, the absolute value is 7.
To express mathematically the absolute values of positive and negative numbers,
you enclose the number in vertical bars.
j 7 7
j 7 7
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