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Significant Digits – Da Rules

Significant Digits – Da Rules. The leftmost non-zero digit is significant and is in fact the most significant digit in the number. If the number has no decimal point, the rightmost non-zero digit is significant and is in fact the least significant.

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Significant Digits – Da Rules

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  1. Significant Digits – Da Rules The leftmost non-zero digit is significant and is in fact the most significant digit in the number. If the number has no decimal point, the rightmost non-zero digit is significant and is in fact the least significant. If the number does have a decimal point, the least significant digit is the rightmost digit (which may be zero). The number of significant digits of a number is the number of digits from the most to the least significant.

  2. Significant Digits – How Many? 63 0.63 0.06301 0.00630 630 630.0

  3. Significant Digits – How Many? 63 0.63 0.06301 0.00630 630 630.0 2

  4. Significant Digits – How Many? 63 0.63 0.06301 0.00630 630 630.0 2 2

  5. Significant Digits – How Many? 63 0.63 0.06301 0.00630 630 630.0 2 2 4

  6. Significant Digits – How Many? 63 0.63 0.06301 0.00630 630 630.0 2 2 4 3

  7. Significant Digits – How Many? 63 0.63 0.06301 0.00630 630 630.0 2 2 4 3 2

  8. Significant Digits – How Many? 63 0.63 0.06301 0.00630 630 630.0 2 2 4 3 2 4

  9. Significant Digits – Scientific Notation 63 0.63 0.06301 0.00630 630 630.0

  10. Significant Digits – Scientific Notation 63 0.63 0.06301 0.00630 630 630.0 6.3 x 101

  11. Significant Digits – Scientific Notation 63 0.63 0.06301 0.00630 630 630.0 6.3 x 101 6.3 x 10-1

  12. Significant Digits – Scientific Notation 63 0.63 0.06301 0.00630 630 630.0 6.3 x 101 6.3 x 10-1 6.301 x 10-2

  13. Significant Digits – Scientific Notation 63 0.63 0.06301 0.00630 630 630.0 6.3 x 101 6.3 x 10-1 6.301 x 10-2 6.30 x 10-3

  14. Significant Digits – Scientific Notation 63 0.63 0.06301 0.00630 630 630.0 6.3 x 101 6.3 x 10-1 6.301 x 10-2 6.30 x 10-3 6.3 x 102

  15. Significant Digits – Scientific Notation 63 0.63 0.06301 0.00630 630 630.0 6.3 x 101 6.3 x 10-1 6.301 x 10-2 6.30 x 10-3 6.3 x 102 6.300 x 102

  16. Significant Digits • In multiplication, division, powers and roots, the result must only have as many significant digits as those of the number with the least number of significant digits entering the operations. • In addition and subtraction, the answer must have the same number of digits after the decimal point as the number in the problem with the least number of digits after the decimal.

  17. Significant Digits • Always use the numbers that you have been given and round THE ANSWER to correct number of significant digits • Carry all digits in your calculator, write the answer in significant digits • Defined conversions don’t count (1cm = 10mm) • Constants or derived conversions do (s = 3.00 x 108 m/s) (1 AU = 1.5 x 106 km)

  18. Line of Best Fit Video

  19. Line of Best Fit • Choosing a line which goes through as many data points as possible in such a way that the distances between the line and the points on one side of it are, on average, the same as the distances between the line and points on the other side of it.

  20. Line of Best Fit • The line of best fit will ideally pass through the vertical and horizontal error bars • NEVER connect the dots with straight-line segments • Let Excel do it • Works on curves too • Let Excel do it

  21. Line of Best Fit - Slope • The slope of the line of best fit gives you the best relationship between your two variables • To find the slope, • Use the line of best fit, NOT YOUR DATA POINTS! • Take points as far away from each other as possible

  22. Line of Best Fit – Min/Max Slope - Video

  23. Line of Best Fit – Min/Max Slope • Used to determine the uncertainty of your slope • Slopes must cross through the error ‘areas’ rectangles formed by uncertainty of each variable • If not, then use standard error propagation (Lsn 1-5)

  24. Summary Review • Are you able to: • State the various types of errors that may arise in the measurement of a physical quantity? • State the difference between accuracy and precision? • Draw a line of best fit? • Appreciate the importance of significant digits?

  25. Assessment Statements • The SI System of Fundamental and Derived Units • State the fundamental units in the SI system. • Distinguish between fundamental and derived units and give examples of derived units. • Convert between units of quantities. • State units in the accepted SI format. • State values in scientific notation and in multiples of units with appropriate prefixes.

  26. Assessment Statements • Uncertainty and Error in Measurement • Describe and give examples of random and systematic errors. • Distinguish between accuracy and percision • Explain how the effects of random errors may be reduced. • Calculate quantities and results of calculations to the appropriate number of significant digits.

  27. Homework # 1-6 odds and evens

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