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Significant Figures

Significant Figures. How Much Liquid is in Each Graduated Cylinder?. Measurement Plastic Ruler. Accuracy: Object is more than 12cm and less than 12.5 cm.

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Significant Figures

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  1. Significant Figures

  2. How Much Liquid is in Each Graduated Cylinder?

  3. Measurement Plastic Ruler • Accuracy: Object is more than 12cm and less than 12.5 cm. • Precision: The smallest marking represents 0.5cm, so you can estimate to the nearest 0.1 cm. The length of the object would be accurately and precisely recorded as 12.4cm. • Uncertainty: 12.4 +/- 0.25cm

  4. MeasurementMetalRuler • Accuracy: Object is more than 12.3cm and just less than 12.4 cm. • Precision: The smallest marking represents 0.1cm, so you can estimate to the nearest 0.01 cm. The length of the object would be accurately and precisely recorded as 12.35cm. • Uncertainty: 12.35 +/- 0.05cm

  5. - Metric Measurements -every measurement contains error! • Every piece of equipment has a certain range of uncertainty. (ex. +/- 0.2 g) This will be given on the piece of equipment. Most equipment is created in factories, so there are bound to be some mistakes! • Every measurement contains estimation equal to a maximum of one half of the smallest unit on the piece of equipment. (ex. If a graduated cylinder is marked off in whole mL, you must estimate volumes in between mL lines.)Your measurement should go one decimal place beyond what is known.

  6. Accuracy vs. Precision Accuracy • How close your measurement is to an accepted value for that measurement. • Depends on how carefully the measurement was made. • Precision-2 Meanings • The repeatability (2.2, 2.3, 2.2) of a measurement. • The number of significant digits (2.2 vs. 2.20475) in the measurement. • Depends on the equipment used.

  7. Accuracy • When throwing darts, a bulls eye is considered accurate. • In an experiment, you could also achieve accuracy with several measurements that when averaged closely match the accepted value.

  8. Precision • When throwing darts, precision occurs when you consistently hit the same spot. • In lab, getting data points that are close together shows precision. • A reading with many digits beyond the decimal also shows precision.

  9. Accuracy vs. Precision Who or What is to blame…. • If values are precise but not accurate? • If the values are not precise but only a few are accurate? How can precision and accuracy help in trying to solve an experimental problem? And where do I know where to stop when I want to round numbers???

  10. Significant Figures • Significant Figures: a system for representing measured values with the correct degree of accuracy. Its main purpose is to know how much to round off answers calculated from any measurement. A "significant" figure is a figure that is considered accurate. • Remember! Every time you make a measurement, you record all of the certain digits and one estimated digit 200.54 g

  11. Rules for Sig Figs • Non zeros are always significant. • Zeros between non zeros are significant. • Zeros at the end of significant digits following a decimal point are significant. *They show precision in measurement. 4) Place keeper zeros are NOT significant. • Zeros preceding significant digits. • Zeros following significant digits without a decimal point.

  12. Try These Examples 7.05940 Final zero significant (follows decimal point) 6 significant digits 0.00135 Leading zeros Not significant (place keepers) 3 significant digits 20,400 Final zeros Not significant (place keepers – no decimal) 3 significant digits

  13. Remember…. • When measuring an object, the significant figures of the number should go one place beyond what is KNOWN. Volume:4.33

  14. Rounding • You may be asked to frequently round numbers in sig figs. This is done when you are not able to measure a number (it is just given to you). • Example: Round the following number to the appropriate significant figures. • A) 5486 – 2 sig figs • B) 31,947.972 – 3 sig figs • C) 4367800.00 – 4 sig figs

  15. Rounding and Scientific Notation • Numbers are typically expressed as the product of a number between 1 and 10 raised to a power. Ex: 1350 is written as 1.35 x 103 0.002 is written as 2 x 10-3 • This concept can be applied to numbers with sig figs. Ex: Round 31,947.972 to 3 sig figs and express it in scientific notation. 31,947.972 (w/ 3 sig figs) = 31900.000 = 3.19 x 104

  16. Well, What if I am actually calculating numbers that have different sig figs? What do I do?

  17. Sig Figs and Calculations • Addition and Subtraction • The answer must have the number of digits to the right of the decimal point as there are in the measurement having the fewest digits to the right of the decimal point. • Hint: Line up your decimal places, add the numbers normally, and THEN worry about sig figs!! Ex: 17.20 Answer: 47.9 4.137 + 26.6 47.937

  18. Sig Figs and Calculations • Multiplication and Division • The answer can have no more sig figs than are in the measurement with the fewest number of sig figs • Hint: Multiply your numbers normally, and then make sure the sig figs in your answer are for the “lesser” number. Ex: 14.3 (3 sig figs) Answer: 1.0200 (5 sig figs) 0.07 x 0.005 (1 sig fig) 0.07293

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