Quantitative Measurements Numerical Units Examples: 50.5 cm, 35° C, 2.5 g/cm3

Scientific Notation Used because of very small and very large numbers M x 10n M ≥ 1 and < 10 n is a whole number 5400 = 5.4 x 103 0.0017 = 1.7 x 10-3

Rules Move decimal to left- exponent more positive Move decimal to right- exponent more negative Numbers greater then 10- exponent positive Numbers less than 0- exponent negative

Addition/ Subtraction Must make exponents the same Add or subtract numbers & keep same exponent 6.7 x 104 + 3 x 103 6.7 x 104 + 0.3 x 104 7.0 x 104

Multiplication Multiply numbers and add exponents (2 x 102) (4 x 103) = 8 x 105

Division Divide numbers and subtract exponents (6 x 105) /(3 x 102) =

Practice 1. 0.000137 in scientific notation 1.37 x 10-4

Multiply (3.9 x 107) (1.2 x 102)= 4.7 x 109 Divide (8.4 x 10-3) / (4.7 x 104)= 1.8 x 10-7

Add (2.3 x 102)+(1.9 x 101) +(1.7 x 103) 1.7 x 103 0.23 x 103 +0.019 x 103 1.949 x 103

Subtract (3.1 x 10-3) –(8.5 x 10-2) 0.31 x 10-2 - 8.5 x 10-2 - 8.19 x 10-2