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Measurement & Calculations

Measurement & Calculations. Overview of the Scientific Method. OBSERVE. FORMULATE HYPOTHESIS. TEST. THEORIZE. PUBLISH RESULTS. CONVERSION FACTORS. Uncertainty in Measurement. •Two kinds of numbers in scientific work: exact numbers (those whose values are known exactly) and

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Measurement & Calculations

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  1. Measurement & Calculations

  2. Overview of the Scientific Method OBSERVE FORMULATE HYPOTHESIS TEST THEORIZE PUBLISH RESULTS

  3. CONVERSION FACTORS

  4. Uncertainty in Measurement •Two kinds of numbers in scientific work: exact numbers (those whose values are known exactly) and inexact numbers (those whose values have some uncertainty). •Exact numbers: counts (e.g. students in this classroom), numbers by definition (e.g. 1 m = 100 cm, 1 in = 2.54 cm). •Numbers obtained by measurement are always inexact.

  5. PRECISION OF CALCULATIONS How close are your calculated answers to the known or accepted value

  6. Rules for Significant Figures • Non-zero digits are always significant. • Any zeros between two significant digits are significant. • A final zero or trailing zeros after the decimal are significant. • Zeros that are holding decimal places are NOT significant

  7. Significant Figures in Calculations The result of calculation using measured numbers should reflect the precision of the original measurements. The significant figures in calculation should follow the following rules: Addition and Subtraction The answer cannot have more decimal places than the measurement with the fewest number of decimal places. e.g. 4 + 1.45 +12.4 = 17.85 round off to 18 Multiplication and Division The answer cannot have more significant figures than the measurement with the fewest numbers of significant figures. e.g. 6.221 x 5.2 = 32.3492 􀃆 round off to 32

  8. Examples (continued) Problem. Perform the calculation and express your answer to the correct number of sig. fig. (a)(12.4 – 9.45) / 0.2212 = 2.95 / 0.2212 = 13.336…  round off to 13. In sequential operations, the correct rule must be applied to each operation. Carry all numbers through the calculation and round at the end. (b) (0.0045 x 20,000.0) + (2813 x 12) = 90 + 33756 =0.0090 x 104 + 3.3756 x 104 = 3.3846 x 104  round off to 3.4 x 104

  9. Scientific Notation Scientific notation is used to eliminate the potential ambiguity of whether the zeros at the end of a number are significant. The significant figure information is in the coefficient and decimal point information is in the exponent. e.g. 10,300 is written 1.03x104 (3 sig. fig.) 10,300 is written 1.030x104 (4 sig. fig.) 10,300 is written 1.0300x104 (5 sig. fig.) Note that in scientific notation, a correctly written number has a single nonzero digit to the left of the decimal point. Exercise: How many significant figures are in each of the following measured numbers? (a) 4.003, (b) 6.023 x 1023, (c) 5000

  10. Accuracy: How close you are to the actual value Depends on the person measuring Calculated by the formula: % Error = (YV – AV) x 100 ÷ AV Where: YV is YOUR measured Value&AV is the Accepted Value Precision: How close the measurements are to each other Depends on the measuring tool Determined by the number of significant digits Accuracy & Precision

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