 # Observation, Measurement and Calculations Cartoon courtesy of NearingZero.net.

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Observation, Measurement and Calculations Cartoon courtesy of NearingZero.net

Steps in the Scientific Method 1.Observations -quantitative - qualitative 2.Formulating hypotheses - possible explanation for the observation 3.Performing experiments - gathering new information to decide whether the hypothesis is valid whether the hypothesis is valid

Outcomes Over the Long-Term Theory (Model) - A set of tested hypotheses that give an overall explanation of some natural phenomenon. overall explanation of some natural phenomenon. Natural Law - The same observation applies to many different systems different systems - Example - Law of Conservation of Mass

Law vs. Theory A law summarizes what happens  A law summarizes what happens  A theory (model) is an attempt to explain why it happens.

Nature of Measurement Part 1 - number Part 2 - scale (unit) Examples: 20 grams 6.63 x 10 -34 Joule seconds Measurement - quantitative observation consisting of 2 parts consisting of 2 parts

Systems of measurement Metric system vs English system »Metric (SI) International system –Standardized -international –consistent base units –multiples of 10 »English (US) system –non-standard -only US –no consistent base units –no consistent multiples

Using the Metric system Prefixes for multiples of 10 »T - G - M -k h d (base) d c m - -  - - n - -p »Tera 10 12 – Giga 10 9 – Mega 10 6 – kilo 10 3 – hecto 10 2 – deka 10 1 – base – deci 10 -1 – centi 10 –2 - milli 10 –3 – micro 10 –6 – nano 10 –9 – pico 10 -12 »move the decimal to convertmove the decimal to convert

The Fundamental SI Units

SI Prefixes Common to Chemistry PrefixUnit Abbr.Exponent Kilok10 3 Decid10 -1 Centic10 -2 Millim10 -3 Micro  10 -6

400 m = ? cm Moving the decimal For measurements that are defined by a single unit such as length, mass, or liquid volume and later in the course, power, current, voltage, etc., simply move the decimal the number of places indicated by the prefix. 400 m = ? cm40,000 cm 75 mg = ? g 0.075 g 0.025  m = ? mm 0.000025 mm

Metric –multiples of 10 –move decimal –*area - move twice –*volume - move three times English Metric –conversion factors –proportion method –unit cancellation method Converting measurements

Common Conversions 1 kilometer =.621 miles 1 meter = 39.4 inches 1 centimeter =.394 inches 1 kilogram = 2.2 pounds 1 gram =.0353 ounce 1 liter = 1.06 quarts

Uncertainty in Measurement A digit that must be estimated is called uncertain. A measurement always has some degree of uncertainty.

Why Is there Uncertainty?  Measurements are performed with instruments  No instrument can read to an infinite number of decimal places

Precision and Accuracy Accuracy refers to the agreement of a particular value with the true value. Precision refers to the degree of agreement among several measurements made in the same manner. Neither accurate nor precise Precise but not accurate Precise AND accurate

Rules for Counting Significant Figures Nonzero integers always count as significant figures. 3456 has 4 sig figs.

Rules for Counting Significant Figures Zeros - Captive zeros always count as significant figures.(zeros in between nonzeros) 16.07 has 4 sig figs.

Rules for Counting Significant Figures Zeros - Leading zeros do not count as significant figures. 0.0486 has 3 sig figs.

Rules for Counting Significant Figures Zeros Trailing zeros are significant only if the number contains a decimal point. 9.300 has 4 sig figs.

Rules for Counting Significant Figures Any whole number that ends in zero and does not have a decimal in unclear or unknown. 10 unknown 20. Has 2 significant figures

Sig Fig Practice #1 How many significant figures in each of the following? 1.0070 m  5 sig figs 17.10 kg  4 sig figs 100,890 L  unclear 3.29 x 10 3 s  3 sig figs 0.0054 cm  2 sig figs 3,200,000  unclear

Rules for Significant Figures in Mathematical Operations Multiplication and Division: # sig figs in the result equals the number with the least number of sig figs. 6.38 x 2.0 = 12.76  13 (2 sig figs)

Sig Fig Practice #2 3.24 m x 7.0 m CalculationCalculator says:Answer 22.68 m 2 23 m 2 100.0 g ÷ 23.7 cm 3 4.219409283 g/cm 3 4.22 g/cm 3 0.02 cm x 2.371 cm 0.04742 cm 2 0.05 cm 2 710 m ÷ 3.0 s 236.6666667 m/sunclear 1818.2 lb x 3.23 ft5872.786 lb·ft 5.87 x 10 3 lb·ft 1.030 g ÷ 2.87 mL 2.9561 g/mL2.96 g/mL

Rules for Significant Figures in Mathematical Operations Addition and Subtraction: The number of decimal places in the result equals the number of decimal places in the number with the least decimal places. 6.8 + 11.934 = 18.734  18.7 (3 sig figs)

Sig Fig Practice #3 3.24 m + 7.0 m CalculationCalculator says:Answer 10.24 m 10.2 m 100.0 g - 23.73 g 76.27 g 76.3 g 0.02 cm + 2.371 cm 2.391 cm 2.39 cm 713.1 L - 3.872 L 709.228 L709.2 L 1818.2 lb + 3.37 lb1821.57 lb 1821.6 lb 2.030 mL - 1.870 mL 0.16 mL 0.160 mL

Significant Figures Rules for rounding off numbers (1) If the digit to be dropped is greater than 5, the last retained digit is increased by one. For example, 12.6 is rounded to 13. (2) If the digit to be dropped is less than 5, the last remaining digit is left as it is. For example, 12.4 is rounded to 12.

(3) If the digit to be dropped is 5, and if any digit following it is not zero, the last remaining digit is increased by one. For example, 12.51 is rounded to 13

Significant Figures (4) If the digit to be dropped is 5 and is followed only by zeros, the last remaining digit is increased by one if it is odd, but left as it is if even. For example,

11.5 is rounded to 12, 12.5 is rounded to 12. This rule means that if the digit to be dropped is 5 followed only by zeros, the result is always rounded to the even digit. The rationale is to avoid bias in rounding: half of the time we round up, half the time we round down.

In science, we deal with some very LARGE numbers: 1 mole = 602000000000000000000000 In science, we deal with some very SMALL numbers: Mass of an electron = 0.000000000000000000000000000000091 kg Scientific Notation

Imagine the difficulty of calculating the mass of 1 mole of electrons! 0.000000000000000000000000000000091 kg x 602000000000000000000000 x 602000000000000000000000 ???????????????????????????????????

Scientific Notation: A method of representing very large or very small numbers in the form: M x 10n M x 10n  M is a number between 1 and 10  n is an integer

2 500 000 000 Step #1: Insert an understood decimal point. Step #2: Decide where the decimal must end up so that one number is to its left up so that one number is to its left Step #3: Count how many places you bounce the decimal point the decimal point 1234567 8 9 Step #4: Re-write in the form M x 10 n

2.5 x 10 9 The exponent is the number of places we moved the decimal.

0.0000579 Step #2: Decide where the decimal must end up so that one number is to its left up so that one number is to its left Step #3: Count how many places you bounce the decimal point the decimal point Step #4: Re-write in the form M x 10 n 12345

5.79 x 10 -5 The exponent is negative because the number we started with was less than 1.

Direct Proportions  The quotient of two variables is a constant  As the value of one variable increases, the other must also increase  As the value of one variable decreases, the other must also decrease  The graph of a direct proportion is a straight line

Inverse Proportions  The product of two variables is a constant  As the value of one variable increases, the other must decrease  As the value of one variable decreases, the other must increase  The graph of an inverse proportion is a hyperbola