Transcript 1.7 Scientific Notation

1.7
Scientific Notation
A number is written in scientific
notation when it is expressed in the
form
where the absolute value of a is greater
than or equal to 1 and less than 10, and
n is an integer.
If n is positive, move the decimal point
in a to the _______________ n places.
If n is negative, move the decimal
n
point in a to the _______________
places.
Example 1:
Write each number in decimal notation:
A) -2.6 x 109
B) 3.017 x 10-6
Example 2:
Write each number in scientific
notation:
A) 5, 210, 000, 000
B) -0.00000006893
Example 3:
In 2005, the federal cost of social
security was $519 billion. Express this
amount in scientific notation.
Computations with Numbers
in Scientific Notation
Multiplication:
(a x 10n)(b x 10m) = (a x b) x 10n + m
Division:
a x 10n = a x 10m - n
b x 10m
b
After the computation is completed, the answer
Example 4:
Perform the indicated computations,
writing the answers in scientific
notation:
A)
(7.1 x 105)(5 x 10-7)
Example 4 continued . . .
B) 1.2 x 106
3 x 10-3
Example 5:
In 2004, the U.S. government collected
2.02 x 1012 dollars in taxes. At that
time, the U.S. population was
approximately 295 million or 2.95 x 108.
Find the per capita tax, rounded to the
nearest dollar, in 2004.
Example 6:
A futuristic spacecraft traveling at
1.55 x 103 miles per hour takes 20, 000
hours (about 833 days) to travel from
Venus to Mercury. What is the distance
from Venus to Mercury?
(Hint: d = rt)
Homework:
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