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Numbers in Science

Numbers in Science. Taking and using accurate measurements.

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Numbers in Science

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  1. Numbers in Science Taking and using accurate measurements M J Cook

  2. This presentation is 4 different note taking pages in one – watch for the beginning and ending of each page. Remember: notes are input/right side pages ONLY. If you are using this as make-up work, please see Ms. Cook for missed worksheets that go along with these notes. M J Cook

  3. Beginning of Page 1: Numbers in ScienceTaking Measurements 2 kinds of numbers in Science: 1. Exact – counted or by definition examples – stack of coins - 3ft = 1 yard accuracy – infinitely accurate (no estimation involved – there are 3.00000 ft in a yard) M J Cook Continue Page 1

  4. Numbers in ScienceTaking Measurements 2. Measured numbers – involve estimation examples – ruler, triple beam balance, graduated cylinder accuracy – only as accurate as instrument used M J Cook Continue Page 1

  5. Read each measurement below to the accuracy of the instrument – remember to read to the smallest mark and estimate the next number. • Which one is more accurate? Why? M J Cook End Page 1

  6. Beginning of Page 2: Numbers in ScienceSignificant Figures • All measured numbers are considered “significant” (They all count as significant since somebody had to read them.) M J Cook Continue Page 2

  7. Counting Significant Figures(sig. figs) • Non zero numbers (1-9) – always “significant”, someone read them • Zeros only count if they were measured • “sandwiched” zeros (102 – 3 sig figs) • at the end of a number with a decimal (122.0 – 4 sig figs) M J Cook End Page 2

  8. Beginning of Page 3: Numbers in ScienceSignificant Figures and Calculations - Calculated answers can NOT be more accurate than the numbers used in the calculations M J Cook Continue Page 3

  9. Example • Addition 4.0 g + 3.51 g = 9.91 g (raw numbers) REPORTED ANSWER: 7.5 g M J Cook Continue Page 3

  10. Example • Subtraction 11.625 ml – 2 ml = 9.325 ml (raw numbers) REPORTED ANSWER: 9 ml M J Cook Continue Page 3

  11. Rules for Calculations • Add/subtract – answers round to match measurement with least number of decimal places M J Cook Continue Page 3

  12. Example • Multiplication 73 cm X 21 cm X 45 cm = 68985 cm3 (raw numbers) REPORTED ANSWER: 69000 cm3 M J Cook Continue Page 3

  13. Example • Division 5120 g 30.0 ml = 170.6666667 g/ml (raw numbers) REPORTED ANSWER: 171 g/ml M J Cook Continue Page 3

  14. Rules for Calculations 2. Multiply/divide – answers round to match measurement with least number of significant digits M J Cook End Page 3

  15. Beginning of Page 4: Units in CalculationsDimensional Analysis • Units accompany all measurements – keeping up with units can • Help you convert one quantity to another • Set up a calculation M J Cook Continue Page 4

  16. Conversion Problems Follow these steps to convert: 1. Write down all “=“ statements that will help Example: How many inches are in 1.24 miles? 1. 1 ft = 12 in, 5280 ft = 1 mile M J Cook Continue Page 4

  17. Conversion Problems • Make fractions out of “=“ statements (there are 2 for each – think reciprocals) Example: 2. 1ft and 12 in 12 in 1 ft 5280 ft and 1 mile 1 mile 5280 ft M J Cook Continue Page 4

  18. Conversion Problems • Solve problem – write given amount, with units, on left side of paper – put the number over “1”. Write units you “want” on right. Use fractions that will cancel numerators and denominators across. Example: Step 3 1.24 miles = inches X 5280 ft 1 mile X 1 mile 5280 ft X 12 in 1 ft 1 M J Cook Continue Page 4

  19. Conversion Problems • Do calculations, left to right, numerator divided by denominator, times the next numerator divided by the next denominator Example: Step 3. 1.24 miles X 5280 ft X 12 in = 1 1 mile 1 ft Step 4: 1.24 78566.4 ÷ 1 X 5280 ÷ 1 X 12 ÷ 1 = in M J Cook Continue Page 4

  20. Conversion Problems • Round answer to number of significant digits in original number. Example: 1.24 has significant figures, so… 78566.4 rounds to 3 78600 in M J Cook End Page 4

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