SCIENTIFIC NOTATION

Scientific Notation: coefficient power M. x 10n

3.254 x 103 Scientific Notation: coefficient Power 3.254 x 103 Consists of a number with only ONE DIGIT to the LEFT of the decimal times some power of 10.

Changing from Scientific Notation to Standard Numeral 1. If the exponent is (+): Move the decimal to the right! Examples: 1.5 x 103 = 1.5 0 0 = 1500

Changing from Scientific Notation to Standard Numeral 2. If the exponent is (-): Move the decimal to the left. Examples: 2.63 x 10-3 = 0 0 2. 6 3 = 0.00263

Standard Numeral to Scientific Notation: 1. Whole numbers will have: Positive power of 10 move decimal to left Examples: 8500 = 8 5 0 0. = 8.5 x 103

Standard Numeral to Scientific Notation: 2. Decimal Numbers will have: negative power of 10 move decimal to right Examples: 0.789 = 0.7 8 9 = 7.89 x 10-1

MATHEMATICAL CALCULATIONS USING SCIENTIFIC NOTATION

MULTIPLICATION (1.5 x 103) ( 2.0 X 105) = 3.0 x 108 A. Multiply base numbers B. Add exponents of 10 Example: (1.5 x 103) ( 2.0 X 105) = 3.0 x 108

DIVISION A. Divide base numbers B. Subtract exponents of 10 (numerator - denominator) numerator 4.0 x 102 = 2.0 x 10-2 2.0 x 104 denominator

ADDITION AND SUBTRACTION *Exponents must be the SAME! (6.5 x 102) + (2.0 x 103) + (30.0 x 103) (0.65 x 103) + (2.0 x 103) + (30.0 x 103) 32.65 x 103 = 3.265 x 104

Every answer should be written in correct scientific notation!! 632 x 102 = 6.32 x 104 .0754 x 103 = 7.54 x 101 *Move decimal RIGHT = MORE NEGATIVE *Move decimal LEFT = MORE POSITIVE *ALL DIGITS IN THE COEFFICIENT ARE SIGNIFICANT