Introduction to analysis Data handling, errors and so on

Common Decimal Prefixes Used with SI Units. Prefix Prefix Number Word Exponential Symbol Notation tera T 1,000,000,000,000 trillion giga G 1,000,000,000 billion 10 9 mega M 1,000,000 million 10 6 kilo k 1,000 thousand 10 3 hecto h 100 hundred 10 2 deka da 10 ten one 10 0 deci d 0.1 tenth centi c 0.01 hundredth milli m thousandth micro  millionth nano n billionth pico p trillionth femto f quadrillionth

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 ml has four significant figures, and 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 - Sig digits two 18.00four two five 875,000 three 30,000one five 23, seven three 1,470,000three X 10 7 five 5600two 87,000two 78,002.3 six four X four one six 1,000,000one

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 cm = cm 3 = 23 cm 3 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 ml = ml = ml Example subtracting two volumes: ml ml = ml = ml

Rules for Rounding Off Numbers: 1. If the digit removed is 5 or more, the preceding number increases by 1 : 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 : rounds to 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