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SKILL: USING SCIENTIFIC NOTATION
Numbers with Many Zeros
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Math 7.N.S.1.1
Semiconductor devices are at the heart of the modern personal
computer. Today, tiny chips can contain more than 42,000,000
connections and perform about 3,000,000,000 calculations per
second. Computers have little problem handling such large numbers. Scientists, however, use a scientific notation as a shorthand
way to write large numbers. Scientific notation expresses
a very large or very small number as the product of a number
between 1 and 10 and a power of 10.
Example
Large Number How would you express the number
6,500,000,000—the approximate population of the world as of
July 2005—in scientific notation?
(1) Look at the number and count how many spaces you would
need to move the decimal point to get a number between
1 and 10.
6,
5
9
0
8
0,
0
0
0,
0
0
0
7
6
5
4
3
2
1
(2) Place the decimal point in the space and multiply the number
by the appropriate power of 10. The power of 10 will be equivalent to the number of spaces you moved the decimal point.
ANSWER 6.5 109
Small Number How would you express 0.0000023 in
scientific notation?
(1) Count the number of places you need to move the decimal
point to get a number between 1 and 10. This time you move
the decimal point to the right, not the left.
0.
0
1
0
2
0
3
0
4
0
5
2
3
6
(2) The power of 10 you need to multiply this number by is still
equal to the number of places you moved the decimal point.
Place a negative sign in front of it to indicate that you moved
the decimal point to the right.
ANSWER 2.3 10–6
Answer the following questions.
Chips like the one shown here can be
smaller than a fingernail but contain
millions of independent components.
1. Express the following numbers in scientific notation:
(a) 75,000 (b) 54,000,000,000 (c) 0.0000064
2. Express these numbers in decimal form:
(c) 5.7 10–10
(a) 6.0 1024 (b) 7.4 1022
CHALLENGE What is 2.2 1022 subtracted from 4.6 1022?
Chapter 7: Atomic Structure and the Periodic Table 223
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