# Scientific notation ```Scientific notation
What is scientific notation?
 Numbers are written in the form M &times; 10
^n, Where the factor M is a number
greater than or equal to 1 but less than 10,
and n is a whole number.
 Ex. 6.5 &times; 10⁴ km
 Ex. 9.8 &times; 10&macr;&sup3; g
How to determine scientific notation
 Determine M by moving the decimal point in the
original number to the left or right so that only one
nonzero digit remains to the left of the decimal point.
 Ex. 34000 = 3.4 &times; 104
 Determine n by counting the number of places that you
moved the decimal point. If you moved it to the left, n is
positive. If you moved it to the right, n is negative.
 Ex. 450 = 4.5 &times; 10&sup2;
 Ex. .00091 = 9.1 &times; 10&macr;⁴
Convert numbers into scientific notation
 89000
 68.65
 .00087
 .000000000453
 222.22
notation
 Can be performed only if the values have the same
exponent (n factor).
 Ex. 4.2 &times; 10&sup2; − 2.2 &times; 10&sup2; = 2 &times; 10&sup2;
 If they do not have the same number, adjustments
must be made so the exponent values are equal.
 Ex. 7.001 &times; 10&sup3; + 9.3 &times; 10⁴ = .7001 &times; 10⁴ + 9.3 &times; 10⁴ =
10.0001 &times; 10⁴ = 1.00001 &times; 10⁵
 6.09 &times; 10&macr;&sup1; + 9.2 &times; 10&macr;&sup1;
 7.968 &times; 10⁴ - 9.68 &times; 10&sup3;
 5900 + 7.8 &times; 10&sup3;
 2.31 &times; 10&macr;&sup3; + 6.12 &times; 10&macr;⁵
 1.22 &times; 10&sup1;&sup2; + 1.22 &times; 10&sup1;⁴
 2.34 &times; 10&sup2; + 1.8 &times; 10&macr;&sup1;
Multiplication of scientific notation
 The M factors are multiplied, and the
 Ex. 1.2 &times; 10⁵ &times; 5.45 &times; 10&sup2; = 6.54 &times; 10⁷
Multiply scientific notations
 7.8 X 107 X 1.2 X 105
 6.3 X 10−3 X 7.0 X 105
 6.12 X 103 X 2.1 X 10−23
 6.022 X 1023 X 5.01 X 102
 7.32 X 1.5 X 104
Dividing scientific notation
 The M factors are divided, and the
exponent of the denominator is
subtracted from that of the numerator.
 Ex. 5.44 x 107 &divide; 8.1 &times; 104 = 0.67 x 103
= 6.7 x 102
Divide scientific notations
 9.4&times; 109 &divide; 3.54 &times; 102
 6.32&times; 107 &divide; 7.55 &times; 10−2
 8.655&times; 10−9 &divide; 5.12 &times; 108
 6.54 &divide; 8.66 &times; 10−7
 8.22 &times; 102 &divide; 6.022 &times; 1023
```