1. Significant Figures (Digits) u Exact numbers – pure number/significant digits are NOT applicable u Examples of exact numbers - 10 pennies - 30 students - 1 dozen - 100 %

2. Significant Figures (Digits) u Significant Digits – a number that is part of a measured quantity. Significant digits only apply to measurements. u Some examples of significant digits - 15 cm - 12.5 in - 1.0 qt

3. Significant Figures (Digits) u Rules for using significant digits 1. Apply only to measured quantities 2. Must include units 3. Must reflect the precision of the measuring device.

4. Significant Figures (Digits) u Significant digits apply only to MEASURED quantities a. length b. volume c. mass/weight

5. Significant Figures (Digits) u All non-zero digits are significant a. 531 contains 3 significant digits b. 7318 contains 4 significant digits c. 4 contains 1 significant digit

6. Significant Figures (Digits) u Zeros BETWEEN non-zero digits are significant a. 101 contains 3 significant digits b. 98705 contains 5 significant digits

7. Significant Figures (Digits) u Trailing zeros are NOT significant a. 10 contains 1 significant digit b. 1010 contains 3 significant digits c. 10000 contains 1 significant digit

8. Significant Figures (Digits) u Trailing zeros are NOT significant a. 10 contains 1 significant digit b. 1010 contains 3 significant digits c. 10000 contains 1 significant digit u UNLESS there is a decimal point! a. 10. contains 2 significant digits b. 1010. contains 4 significant digits c. 10000. contains 5 significant digits

9. Significant Figures (Digits) u Zeros AFTER a decimal point are significant a. 10.0 contains 3 significant digits b. 1010.00 contains 6 significant digits

10. Significant Figures (Digits) u Zeros AFTER a decimal point are significant a. 10.0 contains 3 significant digits b. 1010.00 contains 6 significant digits u UNLESS the function of the zero is to locate the decimal point a. 0.01 contains 1 significant digits b. 0.0011 contains 2 significant digits

11. Significant Figures (Digits) u Zeros AFTER a decimal point and AFTER a significant digit are significant a. 0.010 contains 2 significant digits b. 0.0100 contains 3 significant digits c. 0.010010 contains 5 significant digits

12. Significant Figures (Digits) u Non-zero digits BEFORE a decimal point makes all zeros significant a. 1.00 contains 3 significant digits b. 1.010 contains 4 significant digits c. 1.011010 contains 7 significant digits

13. Significant Figures (Digits) u Significant digits do not apply to counting numbers or exact numbers a. 47 people - counting number b. 63 cars entered the race – counting number c. 10 pennies = 1 dime exact number d. 12 apples = 1 dozen

14. Significant Figures (Digits) u Adding with significant digits: 37.25 cm + 4. 387 cm 41.637 cm The answer to this addition can contain only 2 digits beyond the decimal point. The answer to this problem is 41.64 cm, a result based on rounding.

15. Significant Figures (Digits) u Rounding - rounding is the last step in completing a problem and expressing the answer with the correct number of significant digits. Note: Never round until the last step/the final answer.

16. Significant Figures (Digits) u Rules for Rounding u If the rounding digit is greater than 5, increase the preceding digit by 1 u If the rounding digit is less than 5, leave the preceding digit alone u If the rounding digit is 5, then make the preceding digit EVEN!

17. Significant Figures (Digits) u Multiplying with significant digits: 37.25 cm x 4. 387 cm 163.41575 cm 2 The answer to this multiplication can contain only 4 significant digits. Therefore, the answer to this problem is 163.4 cm.

18. Significant Figures (Digits) u Round 47.8485 cm to 2 significant digits

19. Significant Figures (Digits) u Round 47.8485 cm to 2 significant digits u The answer is 48 cm or better 48.cm u Now, round 47.8485 cm to 3 significant digits

20. Significant Figures (Digits) u Round 47.8485 cm to 2 significant digits u The answer is 48 cm or better 48. cm u Now, round 47.8485 cm to 3 significant digits u The answer is 47.8 cm u Now, round 47.8485 to 4 significant digits

21. Significant Figures (Digits) u Round 47.8485 cm to 2 significant digits u The answer is 48 cm or better 48. cm u Now, round 47.8485 cm to 3 significant digits u The answer is 47.8 cm u Now, round 47.8485 cm to 4 significant digits u The answer is 47.85 cm u Finally, round 47.8485 to 5 significant digits

22. Significant Figures (Digits) u Round 47.8485 cm to 2 significant digits u The answer is 48 cm or better 48. cm u Now, round 47.8485 cm to 3 significant digits u The answer is 47.8 cm u Now, round 47.8485 to 4 significant digits u The answer is 47.85 cm u Finally, round 47.8485 cm to 5 significant digits u The answer is 47.848 cm

23. Significant Figures (Digits) u Round 0.092558 to one significant digit

24. Significant Figures (Digits) u Round 0.092558 g to one significant digit u The answer is 0.09 g u Now, round 0.092558 g to three significant digits

25. Significant Figures (Digits) u Round 0.092558 g to one significant digit u The answer is 0.09 g u Now, round 0.092558 g to three significant digits u The answer is 0.0926 g u Now, round 0.092558 g to four significant digits

26. Significant Figures (Digits) u Round 0.092558 g to one significant digit u The answer is 0.09 g u Now, round 0.092558 g to three significant digits u The answer is 0.0926 g u Now, round 0.092558g to four significant digits u The answer is 0.09256 g

27. Exponential Notation u Sometimes we deal with very large or very small numbers. It is difficult to write these numbers with all of the necessary zeros just to show where the decimal point should be. Instead we have developed a technique which allows us to write these numbers in a form which easily shows the number of significant digits and the location of the decimal point. The technique is call exponential notation or scientific notation.

28. Scientific Notation u Scientific Notation (Exponential Notation) writes all numbers using this format: D.DD x 10 p u D represents the significant digits. Note that only one digit remains to the LEFT of the decimal point. The remaining significant digits appear to the right of the decimal point. u P, the power of the base 10, represents the number of spaces that the decimal point had to be moved.

29. Scientific Notation u Write 9600 in scientific notation. u First, determine the number of significant digits in the number. In this case there are two (2). u Since there is no decimal point in this number, place a decimal point at the end of the number: 9600. u Now, move the decimal point to the LEFT until there is only a single digit to the left of the decimal point.

30. Scientific Notation u Now, move the decimal point to the LEFT until there is only a single digit to the left of the decimal point. u The result is: 9.600; since the result should have 2 significant digits, we write the first part as: 9.6 x 10 p u What is the value for p? There are two items that must be considered to determine the value of p. What are they?

31. Scientific Notation u What is the value for p? There are two items that must be considered to determine the value of p. What are they? u (1) How many spaces was the decimal point moved? In our example the answer is 3. u (2) In which direction, Right (-) or Left (+), was the decimal point moved? In our case it was moved to the LEFT. The sign will be +.

32. Scientific Notation u The final notation for our example will be: 9.6 x 10 3 u Write 0.00602 in scientific notation.

33. Scientific Notation u Write 0.00602 in scientific notation. u There are 3 significant digits in this number. u Move the decimal point three spaces. u The result is: 6.02 x 10 -3

34. Unit Factors Conversion Factors Used to convert from one unit to another unit in the same measuring system or a different measuring system Use the “from” and “to” method to determine the values to be placed in the conversion factor

35. Unit Factors 100 cm  1 meter This is an EXACT number - there are exactly 100 cm in 1 meter by definition; the rules for significant digits do not apply Practice using conversion/unit factors

36. Unit Factors