Significant Figures Pacific Atlantic Decimal is Present Decimal is Absent Start on the correct side (is decimal present or absent?) move toward the US First non-zero number and those after all are significant 3.0800 0.00418 7.09 x 10-5 91,600 0.003005 6. 3.200 x 109 7. 250 8. 750, 000, 000 9. 0.0101 10. 0.00800

Sig Figs Multiplying and Dividing Answer must have same number of significant figures as the measurement with the fewest significant figures 3.20 * 3.65 * 2.05 = 23.944 = 23.9 24 * 3.26 = 78.24 = 78 120 * 0.10 = 12.000 = 12 4.84 ÷ 2.4 = 2.016 = 2.0 168 ÷ 58 = 2.8965 = 2.9

Sig Figs Adding and Subtracting Answer must have same # of digits to the right of decimal as the value w/ the fewest digits to the right of decimal (4.32*103) – (1.6*103) = 2.72*103 = 2.7 * 103 28.0 23.538 + 25.68 77.218 = 77.2

Scientific Notation Convenient way of writing very small or large numbers Consists of two parts Number & ten raised to an exponent Exponent is negative, number will be smaller than 1 Exponent is positive, number will be bigger than 1 0.000 000 000 000 000 000 000 162 378 1.62 x 10 -22 136,392,412,792 1.36 x 1011

47,800 0.0035 573 9256 5. 26.23 6. 0.23 7. 0.00036 8. 0.0000501

2.05 x 10-3 4.5 x10-5 1.002 x 108 1.002 x 10-4 9. 4.2 x 103 10 1.12 x 102 1.02 x 101 2.5 x107

Scientific Notation Multiplying Dividing Multiply the first factors Add the exponents (2*103) * (3*103) = 6*106 (4*106) * (2*10-4) = 8*102 Dividing Divide the first factors Subtract the exponents (6*104) ÷ (3*102) = 2*102 (9*103) ÷ (3*10-4) = 3*107 (3- (-4)) = 3+4

6.25 x10-4 / 4.1 x101 4.18 x10-2 / 2.4 x10-2 3.24 x10-4 / 4.8 x10-2 4.1 x103 x 5.2 x 10-4 5.24 x 106 x 6.76 x 102 2.3 x 103 x 9.8 x 10-4

Scientific Notation Adding and Subtracting Exponents MUST BE THE SAME before doing the math! Add the numbers and rewrite x10exponent (2.7*107) + (1.56*105) (270*105) +(1.56*105) = 271.56*105 = 2.7 * 107 (8.3*108) – (4.1*106) (830*106) – (4.1*106) = 825.9 *106 = 8.3 *108

0.0256 + 0.0032 4.1 x105 – 2.8 x 102 3.1 x105 + 5.2 x103

WebAssign rounding sig figs Round to four sig figs 84791 kg 36.8152 g 226.85 cm 5.1676 m

Graphs Visual display of data

Setting up the Graph Adjust your scale to ensure the graph occupies the most space Your values need to increase at a steady rate (for example count by 2)

Setting up the graph… Y axis X axis Always dependent variable Always on vertical axis Y axis X axis Always on horizontal axis Always independent variable

Which is dependent variable? Amount of fertilizer Growth rate of plants Number of years Increase in population Inches of rain that fell Month rainfall occurred Amount due on cell phone bill Minutes used

Interpolation Finding an unknown point between 2 measured points B C A

Extrapolation Finding an unknown point that is outside of 2 measured points B C A

Best fit line line that averages the data points DOES NOT MEAN CONNECT THE POINTS