| CHIMIE 122 LECTURE
Significant Figures, Scientific Notation, and Dimentional Analysis - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - PRECISION VERSUS ACCURACY: precision = how measurements agree. accuracy = how close measurement is to true value. 1. high precision & high accuracy 2. high precision & low accuracy 3. low precision & high accuracy 4. low precision & low accuracy - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - SIGNIFICANT FIGURES: In recording a measurement, write all the numbers with certainty plus the FIRST NUMBER WITH UNCERTAINTY. Illustrate "uncertainty" by reading the muniscus on a graduated cylinder. NOTE: ZEROS used to "place" the decimal are NOT significant figures. 0.015 grams = 2 SF 1.500 grams = 4 SF 1.5 grams = 2 SF EXACT NUMBERS = definitions (not measurements). Exact numbers have "infinite" numbers of significant figures. 2.54 cm = 1 inch - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - HOW MANY SIGNIFICANT FIGURES ARE RETAINED IN ADDITION/SUBTRACTION: When adding or substracting numbers, all numbers must have the same units. The answer can have no more decimals than the measurement with the fewest DECIMALS. 254 ml 254 ml 25.4 ml - 54.1 ml 2.54 ml ===== ====== 199.9 ml 281.94 ml ??? ??? - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - HOW MANY SIGNIFICANT FIGURES ARE RETAINED IN MULTIPLICATION/DIVISION The answer can have no more decimals than the measurement with the fewest SIGNIFICANT FIGURES. (231.54 * 43)/433.4 = 22.972358 ??? - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - SCIENTIFIC NOTATION: Used to express very large or very small numbers as decimal number between 1 and 10 times a power of 10. 133 000 grams = 1.33 x 105 grams Positive exponent tells how many spaces to move the decimal to the right to convert to a decimal number. 0.000 133 grams = 1.33 x 10-4 grams Negative exponent tells how many spaces to move the decimal to the left to convert to a decimal number. ADDITION/SUBTRACTION USING SCIENTIFIC NOTATION: To add/substract numbers written in scientific notation, all number must have THE SAME EXPONENT. 2.54 x 105 grams + 2.54 x 103 grams = 256540 First convert to same exponent. NOTE: if decimal gets larger/exponent gets smaller. If decimal gets smaller/exponent gets larger. Second decide how many significant figures to report. MULTIPLICATION/DIVISION USING SCIENTIFIC NOTATION: Multiplication: multiply the decimals, add exponents, use correct SF 1.35 x 10-5 times 2.35 x 103= 0.031725 ??? Division: divide the decimals, subtract exponents, use correct SF 1.35 x 10-5 divide by 2.35 x 103= 5.745 x 10 -9 ??? - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - UNITS AND PREFIXES: Unit prefixes can be used to make measurement recording easier. kilo = 1000 centi = 0.01 milli = 0.001 micro = 0.000 001 nano = 0.000 000 001 Write an equivalency statement using each of these prefixes. - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Use DIMENSIONAL ANALYSIS to convert units. 1. Identify definition or equivalency statement. 2. multiply so that undesired unit is canceled. 133 000 grams = 133 kg Use dimensional analysis to convert this. 0.000 133 grams = 0.133 mg Use dimensional analysis to convert this. 0.000 133 grams = 133 ug Use dimensional analysis to convert this. - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - MULTISTEP CALCULATIONS USING DIMENSIONAL ANALYSIS: Report the answer to the following calculation using the correct number of significant figures and the correct units. 5431.25 ml * 1.23 grams/ 1000 ml * 1 mole/ 24.1 grams = 0.2771966 number??? units??? - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - |