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Significant Figures

Significant Figures. How to determine and use the proper sig. figs. What is a significant figure?. There are 2 kinds of numbers: Exact numbers Measured numbers. What is a significant figure?. 1) Exact: don’t come in fractions or decimals!!! Ex: humans

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Significant Figures

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  1. Significant Figures How to determine and use the proper sig. figs.

  2. What is a significant figure? • There are 2 kinds of numbers: • Exactnumbers • Measured numbers

  3. What is a significant figure? 1) Exact: don’t come in fractions or decimals!!! • Ex: humans • Ex: bacterial colonies on a petri dish

  4. What is a significant figure? • On the other hand…not everything is so easy…sometimes you have to … Approximate: A close guess that is in the ball park.

  5. When to use Significant figures 2) Measured numbers • Using a tool/ device to measure…you must ask yourself what are the limits of the tool/ device. • Ex:

  6. When to use Significant figures • You could measure Arrow “A” as 3.9cm. But to some mathematicians 3.9cm, or 3.90cm is the same. A

  7. Key difference • But, to a scientist 3.9cm and 3.90cm is NOT the same

  8. Uncertainty The limit of the device! Uncertainty is defined as ½ of the smallest certain unit *You should report the uncertain digit A B

  9. Uncertainty The limit of the device! Uncertainty is defined as ½ of the smallest certain unit What about electronic devices?* Digital Balances: The last digit is uncertain. For example: The mass of the powder is 5.00g ± 0.05 *some electronic devices have published uncertainty, If you have access to the manual, refer to it.

  10. How do I know how many Sig Figs? • Basic Decimal Rules • If no Decimal, then start counting at the first NON zero, and stop counting at the last NON zero! • 30  1 sig fig • 303  3 sig figs • 3030  3 sig figs

  11. How do I know how many Sig Figs? • Basic Decimal Rules • If Decimal, then start counting at the first NON zero, and count until the end! • 3.1  2 sig fig • 3.03  3 sig figs • 3.030  4 sig figs • 0.303  3 sig figs

  12. How many sig figs? • 7 • 40 • 0.5 • 0.00003 • 7 x 105 • 7,000,000 • 1 • 1 • 1 • 1 • 1 • 1

  13. How many sig figs here? • 1.2 • 2100 • 56.76 • 4.00 • 0.0792 • 7,083,000,000 • 2 • 2 • 4 • 3 • 3 • 4

  14. Identify the uncertain digit in each number? • 1.2 • 2100 • 56.76 • 4.00 • 0.0792 • 7,083,000,000 • 1.2 • 2100 • 56.76 • 4.00 • 0.0792 • 7,083,000,000

  15. How many sig figs here? • 3401 • 2100 • 2100.0 • 5.00 • 0.00412 • 8,000,050,000 • 4 • 2 • 5 • 3 • 3 • 6

  16. How would you indicate uncertainty? • 3401 • 2100 • 2100.0 • 5.00 • 0.00412 • 8,000,050,000 • 3401 ±5 • 2100 ±500 • 2100.0 ±0.5 • 5.00 ±0.05 • 0.00412 ±0.00005 • 8,000,050,000 ±50,000

  17. What about calculations with sig figs? • Rule: When adding or subtracting measured numbers, the answer can have no more places after the decimal than the LEAST of the measured numbers.

  18. Add/Subtract examples • 2.45cm + 1.2cm = 3.65cm, • Round off to = 3.7cm • which digit is uncertain? • 3.7

  19. Add/Subtract examples • 7.432cm + 2cm = 9.432 round to  9cm • which digit is uncertain? • 9 cm

  20. Multiplication and Division • Rule: When multiplying or dividing, the result can have no more significant figures than the least reliable measurement.

  21. A couple of examples • 56.78 cm x 2.45cm = 139.111 cm2 • Round to  139cm2 • which digit is uncertain? • 139cm2

  22. A couple of examples • 75.8cm x 9.6cm = ? • Do the math and round to… • Which digit is uncertain? • How would you record uncertainty?

  23. Sig fig Math!!!

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