1 / 20

Numbers in Science

This presentation, created by M.J. Cook, provides four different note-taking pages focused on the importance of accurate measurements and significant figures in science. It covers two types of numbers—exact and measured—along with the rules for calculating significant figures in various mathematical operations. Students will learn how to keep track of units and conversions, ensuring accuracy in their calculations. This material is intended for classroom use, but can also serve as a comprehensive makeup work resource.

samuru
Télécharger la présentation

Numbers in Science

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related