2. Exact Numbers  Are absolutely correct  Obtained by counting  Obtained by definition  Infinite number of significant digits. Example: Counting a stack of 12 pennies Defining 1 day as 24 hours

3. Measured Numbers  Involves estimation  Believed to be correct by the person making and recording a measurement

4. Significant Digits Significant numbers are always measurements and thus should always be accompanied by the measurement's unit.

5. Rule 1 If the digit is NOT a zero, it is significant

6. Significant Digits  Any numbers (that are measurements) other than zero are significant. 123.45 contains five significant digits

7. Rule 2 (a) If the digit IS zero, it is significant if it is a sandwich zero

8. Significant Digits  Any zeros between numbers are significant 1002.05 contains six significant digits

9. Rule 2 (b) If the digit IS a zero, it is significant if it terminates a number containing a decimal place

10. Significant Digits  Any zeros to the left of a number but to the right of a decimal point are NOT significant. 921000. Six significant digits 20.80 Four significant digits

11. Significant Digits  Unless told differently, all zeros to the left of an understood decimal point (a decimal that is not printed) but to the right of the last number are NOT significant  921000  Three significant digits

12. Significant Digits  These zeros are present merely to indicate the presence of a decimal point (they are used as place holders) (these zeros are not part of the measurement). 0.00123 three significant digits

13. Significant Digits 0.00123 grams is equal in magnitude to the measurement 1.23 milligrams. 1.23 has three significant digits, 0.0123 must also have three significant digits.

14. Significant Digits  Any zeros to the right of a number and the right of a decimal point are significant. 0.012300 25.000 both contain five significant digits

15. Significant Digits  The reason for this is that significant figures indicate to what place a measurement is made. Thus the measurement 25.0 grams tells us that the measurement was made to the tenths place. (The accuracy of the scale is to the tenths place.)

16. 453 kg 3 All non-zero digits are always significant.

17. 5057 L 4 Zeros between 2 sig. dig. are significant.

18. 5.00 3 Additional zeros to the right of decimal and a sig. dig. are significant.

19. 0.007 1 Placeholders are not sig.

20. How many significant figures are in each of the following numbers? 1)5.40 ____ 2)210 ____ 3)801.5 ____ 4)1,000 ____ 5)101.0100 ____

21. Calculating with Scientific Notation  Scientific notation is simply a method for expressing, and working with, very large or very small numbers. It is a short hand method for writing numbers, and an easy method for calculations. Numbers in scientific notation are made up of three parts: the coefficient, the base and the exponent. Observe the example below:

22. 5.67 x 10 5  This is the scientific notation for the standard number, 567 000. Now look at the number again, with the three parts labeled. 5.67 x 10 5 coefficient base exponent In order for a number to be in correct scientific notation, the following conditions must be true:  1. The coefficient must be greater than or equal to 1 and less than 10. 2. The base must be 10. 3. The exponent must show the number of decimal places that the decimal needs to be moved to change the number to standard notation. A negative exponent means that the decimal is moved to the left when changing to standard notation.

23. Changing numbers from scientific notation to standard notation.  Ex.1 Change 6.03 x 10 7 to standard notation.  remember, 10 7 = 10 x 10 x 10 x 10 x 10 x 10 x 10 = 10 000 000  so, 6.03 x 10 7 = 6.03 x 10 000 000 = 60 300 000  answer = 60 300 000  Instead of finding the value of the base, we can simply move the decimal seven places to the right because the exponent is 7.  So, 6.03 x 10 7 = 60 300 000

24. Round these numbers to 3 significant digits. A. 1,566,311 B. 2.7651 X 10 -3 C. 84,592 D. 0.0011672 E. 0.07759