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Measurements and Significant Figures

Measurements and Significant Figures. But first: What’s the difference between accuracy and precision? Do they mean the same thing?. Accuracy vs Precision. Accuracy is closeness to the actual value.

margaret-donovan
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Measurements and Significant Figures

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  1. Measurements and Significant Figures

  2. But first: What’s the difference between accuracy and precision?Do they mean the same thing?

  3. Accuracy vs Precision • Accuracy is closeness to the actual value. For example, if a coin has a mass of 10.0701 grams, these would all be accurate masses: 10 g, 10.1g, 10.07 g, 10.070 g But an inaccurate mass would be 75 grams. • Precision comes from the type of measuring tool you use.

  4. Sig Figs measure the degree of precision of a measurement

  5. Precise times are required in close races: 100-meter butterfly results: Michael Phelps 50.58 seconds Milo Cavic 50.59 seconds What is both stopwatches read 51 seconds? They would be accurate, but not sufficiently precise.

  6. In science, a correctly precise measurement includes all digits that are known for sure, plus a digit that is estimated.

  7. For example:

  8. Another example:

  9. But note: • If you’re using a measuring device with a digital display, (like an electronic balance), the rounding has already been done for you. Be sure to copy down every decimal place shown on the digital display.

  10. Calculations involving measurements

  11. Rules for counting sig figs: There are ONLY two rules to remember when counting the # of Sig Figs.

  12. Rule #1: Don’t start counting till you get to a number that isn’t a zero.Rule #2: Once you start counting, don’t stop till you’ve counted all the digits, including zeroes.

  13. And you need to remember a little geography: Where is the Atlantic Ocean, and where is the Pacific Ocean?

  14. How many sig figs are in this number: 273.5200? Ask yourself: Is the decimal point present or absent?

  15. Answer: Present Count from first non-zero number starting at the Pacific side. 273.5200 Once you start counting, you don’t stop!

  16. Examples 2.55 0.2500 100.25

  17. Examples 12.50 0.0050 0.0003

  18. The first step is always to ask yourself: Is the decimal point present or absent? 18,000,000

  19. Answer: Absent Count from first non-zero number moving from the Atlantic side. 18,000,000

  20. Examples 135 100 10500

  21. Examples 350 0.0020 17,500 27.02 2060 135.0

  22. Using sig figs in calculations

  23. Formultiplicationand division:

  24. Your answer can not be more precise than the least precise measurement.

  25. Think of Sloppy Joe

  26. You and your lab partner, Sloppy Joe, have been assigned to find the area of your lab table. You carefully measure the length, and find it to be 233.65 cm. Sloppy Joe glances at the width and suggests that it measures about 100 cm.

  27. 233.65 x 100 = 23365 5 S.F. 1 S.F. 5 S.F.? Answer must be recorded as 20,000 It can have only one sig fig.

  28. Your answer MUST have the same number of sig figs as the factor with the least number of sig figs.

  29. 610 x 6.20 = 3782 2 S.F. 3 S.F. 3800 What is the correct answer?

  30. Example: You calculate the density of an object with mass of 24.300 grams, and volume of 62.5 ml. How many sig figs in your answer?

  31. Foraddition and subtraction

  32. Your answer can not contain more decimal places than the least precise measurement.

  33. Line up the decimal points in the numbers. 2.515 + 1.3 +12.00 =????

  34. 2.515 1.3 + 12.00 15.815 Answer stops here

  35. Sig figs in scientific notation

  36. Scientific notation

  37. The number written before the times sign shows the correct number of SIG FIGS.

  38. Examples 3.50 x 1023 3 S.F. 5.0 x 10 -4 2 S.F. 1 S.F. 3 x 10-4

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