#### Transcript FS1003 Introduction to analysis

Introduction to analysis Data handling, errors and so on Common Decimal Prefixes Used with SI Units. Prefix tera giga mega kilo hecto deka ----deci centi milli micro nano pico femto Prefix Symbol Number Word Exponential Notation T 1,000,000,000,000 trillion G 1,000,000,000 billion M 1,000,000 million k 1,000 thousand h 100 hundred da 10 ten ---1 one d 0.1 tenth c 0.01 hundredth m 0.001 thousandth millionth n 0.000000001 billionth p 0.000000000001 trillionth f 0.000000000000001 quadrillionth 1012 109 106 103 102 101 100 10-1 10-2 10-3 10-6 10-9 10-12 10-15 Rules for Determining Which Digits are Significant All digits are significant, except zeros that are used only to position the decimal point. 1. Make sure that the measured quantity has a decimal point. 2. Start at the left of the number and move right until you reach the first nonzero digit. 3. Count that digit and every digit to its right as significant. Zeros that end a number and lie either after or before the decimal point are significant; thus 1.030 ml has four significant figures, and 5300. L has four significant figures also. Numbers such as 5300 L is assumed to only have 2 significant figures. A terminal decimal point is occasionally used to clarify the situation, but scientific notation is the best! Examples of Significant Digits in Numbers Number 0.0050 18.00 0.0012 83.001 875,000 30,000 5.0000 23,001.00 0.000108 1,470,000 - Sig digits two four two five three one five seven three three Number - 1.3400 X 107 5600 87,000 78,002.3 Sig digits five two two six 0.00007800 four 1.089 X 10-6 0.0000003 1.00800 1,000,000 four one six one Rules for Significant Figures in Answers 1. For multiplication and division. The number with the least certainty limits the certainty of the result. Therefore, the answer contains the same number of significant figures as there are in the measurement with the fewest significant figures. Multiply the following numbers: 9.2 cm x 6.8 cm x 0.3744 cm = 23.4225 cm3 = 23 cm3 2. For addition and subtraction. The answer has the same number of decimal places as there are in the measurement with the fewest decimal places. Add the following volumes: 83.5 ml + 23.28 ml = 106.78 ml = 106.8 ml Example subtracting two volumes: 865.9 ml - 2.8121393 ml = 863.0878607 ml = 863.1 ml Rules for Rounding Off Numbers: 1. If the digit removed is 5 or more, the preceding number increases by 1 : 5.379 rounds to 5.38 if three significant figures are retained and to 5.4 if two significant figures are retained. 2. If the digit removed is less than 5, the preceding number is unchanged : 0.2413 rounds to 0.241 if three significant figures are retained and to 0.24 if two significant figures are retained. 3. Be sure to carry two or more additional significant figures through a multistep calculation and round off only the final answer. Precision and Accuracy Errors in Scientific Measurements Precision - Refers to reproducibility or How close the measurements are to each other. Accuracy - Refers to how close a measurement is to the real value. Systematic error - produces values that are either all higher or all lower than the actual value. Random Error - in the absence of systematic error, produces some values that are higher and some that are lower than the actual value. Constant & Proportional Errors Constant errors Proportional errors 9 8 7 6 5 4 3 2 1 0 10 8 6 4 2 0 0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7