Accuracy and Precision Accuracy – how close a measured value is to the actual (true) value   Precision – how close the measured values are to each other Low Accuracy Low Precision Low Accuracy High Precision High Accuracy High Precision

Types of Error Random Error – when you estimate a value to obtain the last sig fig for any measurement Ex. Measuring the temperature to 1 decimal place using a thermometer Systematic Error – happens due to an inherent error in the measuring system. Ex. using a worn metre stick to measure your height  

Significant Figures Significant figures : the “important” digits in a numerical value. the number contains all the digits that are certain plus one digit that is uncertain.  Example: When a measurement is reported to be 47.5, that means the 4 and 7 are the certain numbers and the 5 is the uncertain numbers. It means that the actual value could be any number between 47.4 – 47.6.

Significant Figure Rules Example Significant Figures 1. Nonzero digits are always significant 1.254 4 sig. fig. 2. Leading zeros (zeros before any nonzero digits) are NOT significant 0.000124 3 sig. fig. 3. Embedded zeros are significant 305.04 5 sig. fig. 4. Zeros’ behind the decimal point are significant 124.00 5 sig fig

State the number of significant figures in each of the followings: Measurement S.F. 967 e. 3.254 b. 1.034 f. 9.3 c. 1.010 g. 2.008 d. 5 h. 8.21

Rules for Sig Figs In Mathematical Operations Multiplying and Dividing Numbers In a calculation involving multiplication or division, the number of significant digits in an answer should equal the least number of significant digits in any one of the numbers being multiplied or divided. e.g. 9.0 x 9.0 =8.1 x 101, while 9.0 x 9 and 9 x 9 = 8 x 101

Rules for Sig Figs In Mathematical Operations Adding and Subtracting Numbers When quantities are being added or subtracted, the number of decimal places (not significant digits) in the answer should be the same as the least number of decimal places in any of the numbers being added or subtracted. e.g. 2.0 + 2.03 = 4.0

Rules for Sig Figs In Mathematical Operations Rounding Rules 1. If the digit after the one you want to keep is greater than 5, then round up. e.g. To obtain 2 sig digs: 3.47 rounds to 3.5; 3.471 rounds to 3.5 2. If the digit after the one you want to keep is less than five, then do nothing. e.g. To obtain 2 sig digs: 3.44 rounds to 3.4; 3.429 rounds to 3.4 3. If the single digit after the one you want is exactly 5, round to the closest even number. e.g. To obtain 2 sig digs: 2.55 is rounded to 2.6; 2.25 is rounded to 2.2 e.g. BUT, 2.251 is rounded to 2.3

Sig Fig Practice #2 Calculation Calculator says: Answer 3.24 m x 7.0 m 22.68 m2 23 m2 100.0 g ÷ 23.7 cm3 4.219409283 g/cm3 4.22 g/cm3 0.02 cm x 2.371 cm 0.04742 cm2 0.05 cm2 710 m ÷ 3.0 s 236.6666667 m/s 2.4 x 102 m/s 1818.2 lb x 3.23 ft 5872.786 lb·ft 5.87 x 103 lb·ft 1.030 g ÷ 2.87 mL 2.9561 g/mL 2.96 g/mL

Sig Fig Practice #3 Calculation Calculator says: Answer 3.24 m + 7.0 m 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 L 709.2 L 1818.2 lb + 3.37 lb 1821.57 lb 1821.6 lb 2.030 mL - 1.870 mL 0.16 mL 0.160 mL

Scientific Notation A method used to express really big or really small numbers. Consist of two parts: 2.34 x 103 The first part of the number indicates the number of significant figures in the value. The second part of the number DOES NOT count for significant figures. This number is ALWAYS between 0 and 10 The 2nd part is always 10 raised to an integer exponent

How its Done 1. Place the decimal point between the first and second whole number, and write ‘x 10’ after the number. e.g. For 12345, it becomes 1.2 x 10 e.g. For 0.00012345, it also becomes 1.2 x 10 2. Indicate how many places you moved the decimal by writing an exponent on the number 10. a) A move to the left means a positive move. e.g. For 12345, it becomes 1.2 x 104 b) A move to the right means a negative move. e.g. For 0.00012345, it becomes 1.2 x 10-4

The Fundamental SI Units In all sciences, calculations are done using SI units (Le Système International d'Unités).

The Fundamental SI Units Physical Quantity Name Abbr. Length meters m Time second s Mass kilogram kg Temperature Kelvin K Amount of Substance mole Mol Electrical Charge Coulomb C

SI Prefixes The international system of units consists of a set of units together with a set of prefixes. Prefix Mega Kilo Hecto Deca base (g, m, L) Deci Centi Milli Micro Symbol M k h da d c m  Factor 106 103 102 101 100 = 1 10-1 10-2 10-3 10-6

Practice! Original Convert to… a) 3.15 m cm e) 955g kg b) 20.0Mg mg f) 178mm c) 75.4L ml g) 650cm mm d)1350mL L h) 88.74ms s

Practice! Original Convert to… a) 3.15 m 315 cm e) 955g 0.955 kg b) 20.0Mg 2.00 x 1010 mg f) 178mm 17.8 cm c) 75.4L 0.0754 mL g) 650cm 6500 mm Or 6.50X103 mm d)1350mL 1.350 L h) 88.74ms 0.08874s

Dimensional Analysis SAMPLE PROBLEMS… Convert 7 years to seconds. REMEMBER: Set up conversion factors to get rid of unneeded units, and to obtain needed units! Conversion can be flipped if needed: 60 s 1min 1min 60 s 1 = =