Scientific Notation
Multiplication:
- The digit terms are multiplied in the normal way and the exponents are added. The end result is changed so that there is only one nonzero digit to the left of the decimal.
- Example: (3.4 x 106)(4.2 x 103) = (3.4)(4.2) x 10(6+3) = 14.28 x 109 = 1.4 x 1010
(to 2 significant figures)
- Example: (6.73 x 10-5)(2.91 x 102) = (6.73)(2.91) x 10(-5+2) = 19.58 x 10-3 = 1.96 x 10-2
(to 3 significant figures)
Division:
- The digit terms are divided in the normal way and the exponents are subtracted. The quotient is changed (if necessary) so that there is only one nonzero digit to the left of the decimal.
- Example: (6.4 x 106)/(8.9 x 102) = (6.4)/(8.9) x 10(6-2) = 0.719 x 104 = 7.2 x 103
(to 2 significant figures)
- Example: (3.2 x 103)/(5.7 x 10-2) = (3.2)/(5.7) x 103-(-2) = 0.561 x 105 = 5.6 x 104
(to 2 significant figures)
Powers of Exponentials:
- The digit term is raised to the indicated power and the exponent is multiplied by the number that indicates the power.
- Example: (2.4 x 104)3 = (2.4)3 x 10(4x3) = 13.824 x 1012 = 1.4 x 1013
(to 2 significant figures)
- Example: (6.53 x 10-3)2 = (6.53)2 x 10(-3)x2 = 42.64 x 10-6 = 4.26 x 10-5
(to 3 significant figures)
Roots of Exponentials:
- Change the exponent if necessary so that the number is divisible by the root. Remember that taking the square root is the same as raising the number to the one-half power.
- Example:
- Example:
