Math 60
4.3: Scientific Notation
Elementary Algebra
Scientific Notation can be used to write super large and super small numbers easily. Scientific Notation looks
like:
 10
.
This portion can be an
approximation rounded
to the nearest tenth or
hundredth.
and always consists of a decimal number (always one digit to the left of the decimal) times an appropriate power
of ten. The “times” or multiply symbol used with Scientific Notation is generally the cross or “” symbol. The
decimal portion of this notation will either be to the nearest tenth or hundredth, however rounding to the nearest
hundredth is more common.
Remember a positive exponent on the power of ten number corresponds to a large number, and a negative
exponent on the power of ten number corresponds to a small number.
If you are unfamiliar with Scientific Notation please consult the official rules on pages 251–252 in your book.
Practice Problems:
Write in Scientific Notation:
1.
0.000053
2.
3, 470, 000, 000
3.
0.00000189
4.
284, 000
Write in Decimal Form (Standard Form):
5.
5.69 108
6.
4.78 107
7.
3.13 104
8.
2.01105
Perform the indicated operation and express each number in Decimal Form (Standard Form):
(Use the following facts when working problems 9 – 11, you will not need all of them)
8.5 4.1  34.85
 34.028.1  275.56
 2.8 7.6  21.28
8.5
 2.07
4.1
34.02
 4.2
8.1
2.8
 0.37
7.6
9.
8.5 10  4.110 
11
6
34.02 10   8.110 
3
10.
11.
4
 2.8 10  7.6 10 
19
19
4.3 Answers – Scientific Notation
1.
5.3 105
2.
3.47 109
3.
1.89 106
4.
2.84 105
5.
569,000,000
7.
31,300
8.
0.0000201
9.
3,485,000
10.
0.42
11.
21.28
6.
0.000000478