Scientific notation
What is scientific notation?
 Numbers are written in the form M × 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 × 10⁴ km
 Ex. 9.8 × 10¯³ 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 × 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 × 10²
 Ex. .00091 = 9.1 × 10¯⁴
Convert numbers into scientific notation
 89000
 68.65
 .00087
 .000000000453
 222.22
Adding and subtracting scientific
notation
 Can be performed only if the values have the same
exponent (n factor).
 Ex. 4.2 × 10² − 2.2 × 10² = 2 × 10²
 If they do not have the same number, adjustments
must be made so the exponent values are equal.
 Ex. 7.001 × 10³ + 9.3 × 10⁴ = .7001 × 10⁴ + 9.3 × 10⁴ =
10.0001 × 10⁴ = 1.00001 × 10⁵
Add or subtract
 6.09 × 10¯¹ + 9.2 × 10¯¹
 7.968 × 10⁴ - 9.68 × 10³
 5900 + 7.8 × 10³
 2.31 × 10¯³ + 6.12 × 10¯⁵
 1.22 × 10¹² + 1.22 × 10¹⁴
 2.34 × 10² + 1.8 × 10¯¹
Multiplication of scientific notation
 The M factors are multiplied, and the
exponents are added algebraically.
 Ex. 1.2 × 10⁵ × 5.45 × 10² = 6.54 × 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 ÷ 8.1 × 104 = 0.67 x 103
= 6.7 x 102
Divide scientific notations
 9.4× 109 ÷ 3.54 × 102
 6.32× 107 ÷ 7.55 × 10−2
 8.655× 10−9 ÷ 5.12 × 108
 6.54 ÷ 8.66 × 10−7
 8.22 × 102 ÷ 6.022 × 1023