Handling Numbers in Chemistry

Transcription

1 Handling Numbers in Chemistry Correct use of significant figures ( SF s ) Correct use of significant figures ( sig figs ) Handling scientific notation Rounding off computational values Knowledge of SI, Metric, and English Units All measured values are limited in scope by the accuracy of the instrument used. When correctly expressed, all measured values contain all the digits which can be read directly plus one estimated digit. The digits in measured values are described as significant figures when they are presented in this fashion. TEST YOUR MEMORY, Counting SF s: 2.35 cm? sf 2.0 in? sf g? sf 2000 g? sf oz? sf.0005 g? sf 2.00 lb? sf 200. ft? sf RECALL THE RULES, COUNT ONLY: 1. All non zero digits: 2.35 cm, 3 SF g, 4 SF 2. All Internal zeros: oz, 4 SF 3. All ending zeros when the decimal point is expressed: 2.00 lb, 3 SF 2.0 in, 2 SF 200. ft, 3 SF

2 DO NOT COUNT AS SIG FIGS: 1. Ending zeros, no decimal point 2000 g, 1 SF 2. All beginning zeros.0005 g, 1 SF GROUP WORK: How many SF s? 1,000 lb g mg 1.00 X 10 3 m in yd 2500 mi 33.0 gal 420. L.0045 cm 150 ml 12 eggs SCIENTIFIC NOTATION Scientific Notation is used to express very large and very small values, and to facilitate expression of some value to correct number of SF s. Scientific Notation is an alternate method of expressing numerical values in which the original value is multiplied or divided by ten until there is only ONE digit to the left of the decimal. The resulting number is multiplied by 10 raised to the appropriate power to restore the worth of the original value. 1,000,000 = 1.00 X 106 (3 SF) or 1 X 106 (1 SF) = 2.70 X 10-5 = x10x10x10x10 27,000 = 2.70 X 104 = 2.70 x10x10x10x10

3 = = = = = 27.0 x 1 = 27.0 x Small Numbers: subtract one from the power of ten for each right move of decimal: In a nutshell: Add +1 to power of ten for each LEFT MOVE Add -1 to power of ten for each RIGHT MOVE = x 100 = 2.7 x = 2.7 X Large Numbers: add one to the power of ten for each left move of decimal: 27,000= 27,000 x 100 = 2.7 x = 2.7 X = 2.70 X = X X 10-5 = X = X 10-3 GROUP WORK Place into Scientific Notation: 95,000 (4 SF s) X X X 10 +4

4 SF S IN CALCULATIONS Calculations Involving SF s Multiplication and Division: When doing calculations involving measured values (always the case in science!), you must limit the number of digits in your results to reflect the degree of uncertainty introduced by these values. You must be familiar with the rules for number of SF s or digits allowed and also with the rules for rounding values down to the allowed number of digits. The final answer in a computation involving these operations should have no more SF s than the value in the original problem with the least number of SF s. Addition and Subtraction: The sum of these operations is allowed no more digits after the decimal than the original value with the least number of digits after the decimal. Rounding off Answers to Correct # SF s If first digit to be dropped is <5, drop it and all following digits, leaving rest of number unchanged. Round off to 4 SF s: = If the first digit to be dropped is >5, drop it and all following digits, but increase the last retained digit by one: Round off to 4 SF s: = Less than five >5

5 If the first digit to be dropped is exactly five, no non zero digits following, even up the resulting rounded-off value: Increase the last retained digit to make it even if it is odd only. SF s in Calculations, Samples: 1.30 in. X.20 in. X in. = in.3 = 7.7 X 10 2 in.3 3 SF 2 SF 4 SF 2 SF allowed Round off to 4 SF s: = = Note: = = in. Since one value has.20 in. no digits after decimal, in. none are allowed! in. = 2962 in. End, Lecture 1 January 2001 METRIC AND SI UNITS Prefixes you should know: M, 1,000,000 (106) X basic unit mega k, 1,000 (103) X basic unit kilo d, 1/10 (10-1) X basic unit deci c, 1/100 (10-2) X basic unit centi m, 1/1000 (10-3) X basic unit milli µ, 1/1,000,000 (10-6) X basic unit micro n, 1/1,000,000,000 (10-9) X basic unit nano p, 1/1,000,000,000,000 (10-12) X basic unit pico