Ch. 2 Measurements and Calculations

Scientific Method Scientific Method: a logical approach to solving problems by observing and collecting data, formulating hypotheses, testing hypotheses and formulating theories that are supported by data. 2-2

Scientific Method System: a specific portion of matter in a given region of space that has been selected for study during an experiment or observation. Hypothesis: a testable statement. Control: experimental conditions that remain constant Variable: experimental conditions that change. 2-3

Scientific Method Steps Observing. Formulating Hypotheses Testing Theorizing Publish Results 2-4

Internationally accepted basic units for scientific measurements. Units of Measurement Quantity: something that has magnitude, size or amount. SI Units: Internationally accepted basic units for scientific measurements. This is helpful so scientists can share and compare data from all over the world! 2-5

Units of Measurement Derived units are obtained from combining the 7 base SI units. Volume: the space occupied by an object. Volume = L x W x H = m3 1 ml = 1 cm3 Density: the ratio of mass to volume D = m/V 2-6

Units of Measurement Conversion factor: a ratio derived from the equality between two different units that can be used to convert from one unit to the other. 1 ft. = 12 inches 1 ft = 1 12 in = 1 12 in 1 ft 2-7

Dimensional Analysis Dimensional Analysis: a mathematical technique that allows you to use units to solve problems involving measurements. Quantity sought = quantity given x conversion factor 18 in = ?ft → 18 in x 1ft = 1.5 ft. 12 in 1 ft = 1 12 in = 1 12 in 1 ft 2-8

Dimensional Analysis 2 Mcookie x 1,000,000 cookies = 2,000,000 cookies 2-9 ex. I have 5 reds, how many blues do I have? (1 red = 4 blues) 5 reds x 4 blues = 20 blues 1 red ex. I have 2 megacookies, how many cookies do I have? 2 Mcookie x 1,000,000 cookies = 2,000,000 cookies 1 Mcookie 2-9

Dimensional Analysis 1) Practice: a)How many milligrams are in 34.0 g? b)How many inches are in a foot? c)How many calories are in 50.0 Joules of energy? d)I have 86 pennies, how many dollars do I have? e) I have $0.86, how many pennies do I have? 2-10

Dimensional Analysis 2) Practice: a) I have 10 gallons of hair gel, how many liters do I have? b) I have $1.00, how many seconds do I have? c) How many inches are in a meter long pixie stick? 2-11

Dimensional Analysis 3) Practice a) How many seconds are in 5.00 hours? b) How many inches are in 4.00 meters? c) How many seconds are in 1.00 years? d) How many cm are in 28.00 ft.? 2-12

Precision and Accuracy Accuracy: the closeness of measurements to the correct or accepted value of the quantity measured. Precision: the closeness of a set of measurements of the same quantity made in the same way. Measurements that are close to the “correct” value are accurate. Measurements that are close to each other are precise. 2-13

Precision and Accuracy 2-14

Experimental Value – Accepted Value X 100% Percent Error Percent Error: Experimental Value – Accepted Value X 100% Accepted Value Example: F.P of water measured = 37oF % Error = 37 – 32 x 100% = 15% error 32 2-15

Significant Figures Significant Figures: in a measurement, the sig figs are all the digits known with certainty plus one final digit, which is estimated. 2-16

Significant Figures Atlantic~Pacific Rule: When a decimal point is present, count sig digs from the first non-zero number from the Pacific side →. When a decimal point is absent, count sig digs from first non-zero number from the Atlantic side ←. Examples: ← 3210 = 3 sig figs → 213.0180 = 7 sig figs 2-17

Significant Figures

Sig Figs 4) Practice: 0.002 523.325 68.25 100 1 1.0000 0.00001 523 1.005 6250 6.02 52000 0.00025 12 0.01000 52001 2-19

Calculations with Significant Figures Sig Figs Calculations with Significant Figures When an exact number is used (a number that is defined, not measured), it does not figure into the sig figs. In x and ÷, the measurement with the fewest # of sig figs determines how many digits the answer is rounded to. In + and -, the number with least # of digits to the right of the decimal determines the number of digits to the right of the decimal. 2-20

Calculations with Significant Figures Sig Figs Calculations with Significant Figures Examples: 253g C x 1mol = 21.083 g C rounds to 21g C 12g C 74.626 - 28.34 46.286 rounds to 46.29 2-21

Calculations with Significant Figures Sig Figs Calculations with Significant Figures Multiplication and Division: 5) Practice: Don’t do the math, how many sig figs would you round your answer to? 530 x 456 = 43 ÷ 5 = ? 21.4 ÷ 500 = ? 45.0 x 3600 = ? 32.1 ÷ 1 = ? 50.000 x 32.8 = ? 2-22

Calculations with Significant Figures Sig Figs Calculations with Significant Figures Addition and Subtraction: how many digits after the decimal point? 6) 45.1 + 32.15 = ? 561 – 34 = ? 78.789 – 56.32 = ? 45.987 + 56.34 = ? 78.4 – 1 = ? 78.000 + 2.47 = ? 2-23

Scientific Notation A method to make large and small numbers easier to work with. The numbers are separated into 2 parts: 1) A number between 1 and 10. 2) A power of 10. Examples: 1000 = 10 x 10 x 10 = 1 x 103 1,000,000 = 10 x 10 x 10 x 10 x 10 x 10 = 1 x 106 0.01 = 1/100 = 1/10 x 10 = 1/102 = 1 x 10-2 2-24

Scientific Notation 0.000135 = 1.35 x 10-4 7035 = 7.035 x 103 15, 361 = 15.361 x 103 NO!!! = 1.5361 x 104 YES!!! 7) Convert the following numbers to scientific notation: 32,450,000 = 0.000024365 = 2-25

Calculations with Sci Notation Addition and Subtraction: the exponents must be made the same for adding and subtracting Multiplication: when multiplying, the first part of the numbers are multiplied and the exponents are added. Division: the first part of the numbers are divided, the exponents are subtracted. 2-26

Proportionality Directly Proportional: two quantities are directly proportional if dividing one by the other gives a constant value. x ∝ y Inversely Proportional: two quantities are inversely proportional if their product is a constant x ∝ 1 y 2-27

Ch. 2 The End 2-28