Chapter 2, Measurements and Calculations 2.1 Scientific Notation 2.2 Units 2.3 Measurements of Length, Volume, and Mass 2.4 Uncertainty in Measurement 2.5 Significant Figures 2.6 Problem Solving and Dimensional Analysis 2.7 Temperature Conversions; An Approach to Problem Solving 2.8 Density LEARN THE RULES

Chapter 2, Measurements and Calculations LEARN THE RULES 2.1 Scientific Notation THE GIVEN After moving decimal points everything is multiplied by 10 to some exponent Take the original number and move the decimal point either right or left so that only one number, (1 to 9) remains to the left of the decimal point and looks like this #.####..... After moving the decimal point count the number of spaces you moved it and make this the exponent (E) attached to the 10 X 10E If you moved the decimal to the left as described in Rule 1 make the Exponent (E) positive (+), if you moved the decimal to the right, make it negative (-)

Chapter 2, Measurements and Calculations LEARN THE RULES 2.1 Scientific Notation 4,237. 35,230. 357, 249. 456.956 34.7890 .0004567 .006790 3 5 2 3 0 3 5 7 2 4 9 4 5 6 9 5 6 3 4 7 8 9 0 0 0 0 4 5 6 7 0 0 6 7 9 0 X 10 ___ 4 5 2 1 -4 -3 / / / / / / 4,237. 4,23.7 1 spot 4,2.37 2 spots 4.237 3 spots X 103

Chapter 2, Measurements and Calculations LEARN THE RULES 2.1 Scientific Notation 4,237. 35,230. 357, 249. 456.956 34.7890 .0004567 .006790 X 10 ___ 3 5 2 3 0 3 5 7 2 4 9 4 5 6 9 5 6 3 4 7 8 9 0 0 0 0 4 5 6 7 0 0 6 7 9 0 X 10 ___ 4,237. 4,23.7 1 spot 4,2.37 2 spots 4.237 3 spots X 10 ___ X 10 ___ X 103 X 10 ___ X 10 ___

English – Metric - International Chapter 2, Measurements and Calculations English – Metric - International 2.2 Units Meter-Liter-Gram 1 .1 .01 .001 10 100 1000 deci centi milli deca hecto kilo 1 x 103 1 x 102 1 x 101 1 x 100 1 x 10-1 1 x 10-2 1 x 10-3 Down Right Up Left English – United States Metric – Most of the remaining Industrialized World International – 1960 Agreement Up Move Decimal Left Down Move Decimal Right INTERNATIONAL Physical Quantity Name of Unit Abbreviation Mass Kilogram kg Length Meter m Time Second s Temperature Kelvin K

Chapter 2, Measurements and Calculations Understanding Metrics 2.3 Measurements of Length, Volume, and Mass Understanding Metrics Meter-Liter-Gram 1 .1 .01 .001 10 100 1000 deci centi milli deca hecto kilo 1 x 103 1 x 102 1 x 101 1 x 100 1 x 10-1 1 x 10-2 1 x 10-3 Down Right Up Left Up Move Decimal Left Down Move Decimal Right Area: (Length) (Width) or LxW EXPRESSED as 1) sq units 2) units squared, or 3) units2 Volume: (Length) (Width) (Height) or LxWxH EXPRESSED as 1) c units, 2) units cubed or 3) units3

Chapter 2, Measurements and Calculations Limited by the Equipment 2.4 Uncertainty in Measurement Most measurements require a level of estimation because of the limits of the device (i.e., Ruler or Graduate Cylinder) Most easily done by estimating the middle distance between two lines of demarcation as a half 1 2 3 4 5 6 Metric Ruler broken into cm 1 cm 1.9 cm Estimating at the mid point of 2.4 cm and 2.5 cm we select 2.45 cm It could in fact be 2.44 cm or 2.46 cm This could be different if another person estimated it There may be multiple measures of several did so What if there were 5 2.45 2.46 2.44 The first two digits in each measurement are the same, 2.4. These are CERTAIN numbers. The third digit, estimated, is UNCERTAIN. All CERTAIN numbers and the first UNCERTAIN number are what we record. These are the SIGNIFICANT FIGURES This ruler, with our estimation is deemed good to the 100ths place and assumed to be + 1 (the estimated number)

Chapter 2, Measurements and Calculations How to Determine 2.5 Significant Figures Rules for Rounding If the digit to be removed <5 the number remains the same (e.g., 1.33 rounds to 1.3) =/> 5 the number increase by 1 (e.g., 1.35 rounds to 1.4) In a series of calculations Carry the extra digits to the end Round the final answer Rules for Significant Figures Non-zero integers Zeros Leading zeros (those appearing before non-zero integers) never count Captive zeros (those appearing between non-zero integers) always count Trailing zeros (those at the right end of non-zero integers) count only when there is a decimal point 100 has 1 sig fig 100. has 3 sig figs Exact Numbers Counted, but not measured Definitions (1 inch = 2.54 cm) Rules for Significant Figures in Calculations Multiplication and Division - Limited to the smallest number of sig figs in the numbers used in the operation (e.g., 4.56 x 1.4 = 6.384 rounded to 2 sig figs because of 1.4, so the answer is 6.4) Addition and Subtraction – The smallest number of decimal places (e.g., 12.11 + 18.0 + 1.013 = 31.123 rounded to 3 sig figs because 18.0 has only 1 decimal place, so the answer is 31.1)

Chapter 2, Measurements and Calculations Give the number of significant figures for the following: A sample of OJ contains 0.0108 g of Vitamin C. ____________ A hair weighed in a crime lab has a mass of 0.0050060 g. ____________ The distance between two points is 5.030 x 103 ft. ____________ 100 runners began the race, but only 60 completed the course. ____________ Without performing the calculation, predict the number of sig figs there in the final answer. Sum of 5.19 1.9 0.842 Difference of 1081 – 7.25 Product of 2.3 x 3.14 Cost of 3 Boxes of candy at $2.50 per box 2 Calculations using significant figures : 5.18 x 0.0208 = 116.83 – 0.33 = (3.60 x 10-3) x (8.123) ÷ 4.3 = 1.33 x 2.8 + 8.41 =

Chapter 2, Measurements and Calculations Give the number of significant figures for the following: A sample of OJ contains 0.0108 g of Vitamin C. ____________ A hair weighed in a crime lab has a mass of 0.0050060 g. ____________ The distance between two points is 5.030 x 103 ft. ____________ 100 runners began the race, but only 60 completed the course. ____________ Without performing the calculation, predict the number of sig figs there in the final answer. Sum of 5.19 1.9 0.842 Difference of 1081 – 7.25 Product of 2.3 x 3.14 Cost of 3 Boxes of candy at $2.50 per box None after Dec 2 3 2 Calculations using significant figures : 5.18 x 0.0208 = 116.8 – 0.33 = (3.60 x 10-3) x (8.123) ÷ 4.3 = 1.33 x 2.8 + 8.41 = 3 aft Dec 1 aft Dec 2 1 aft Dec