BELL RINGER – Complete on a sheet of paper and TURN IN before working on notes!

1. BELL RINGER – Complete on a sheet of paper and TURN IN before working on notes! A student needed to calibrate a graduated cylinder [a device to measure liquids]. She collected the following data: Trail #1 99.98 mL Trial #2 100.02 mL Trial #3 99.99 mL The accepted value of the cylinder’s volume is 100.00 mL. What is the PERCENT ERROR of her measurements?

2. Average = 99.98 + 100.02 + 99.99 = 99.99 • 3 • Error = 99.99 – 100.00 = -.01 • Percent Error = 0.1 x 100 = 0.01 % error • 100.00

3. Significant Figures Dealing with uncertainty in measurements.

4. What values are shown below?

5. Why is it difficult to be certain about some of the measurements you make? • All measurements have some degree of uncertainty due to limits associated with the measuring device. • Generally, uncertainty begins with the LAST DIGIT of the measurement.

6. In a measurement, all the digits known for certain plus the first estimated digit are known as the SIGNIFICANT FIGURES of the measurement. • It is generally accepted that when a measurement is given, all non-zero digits are considered significant. For example 175.4 grams Digits known for certain. First estimated digit.

7. The Problem with Zero • While all non-zero digits are considered significant, ZEROS present a particular problem. • Zeros can be measurements • Zeros can be place holders • How do you decide whether or not a zero is significant?

8. Rules for Significant Figures • 1. ALL non-zero digits are considered significant. • Examples 125.455648 1.1211 • 2. Zeros IN THE MIDDLE OF NUMBERS are significant parts of a measurement. • Examples 5005 120301

9. 3. Zeros AT THE BEGINNING OF A NUMBER are not significant. Examples 0.000003432 0.0021111 • 4. Zeros AT THE END OF A NUMBER are only significant IF THE FOLLOW A DECIMAL or a BAR is placed over a zero… when this occurs, ALL digits up to and including the zero with the bar are significant. _ Example 45.23000 1.000 505.32000 4750000

10. NOTE – If the number is in SCIENTIFIC NOTATION only consider the COEFFICIENT when determining Significant Figures. • Example 4.965 x 1016

11. Practice Problems • Determine how many figures are significant in each of these measurements: • 1. 375 2. 89.000 • 3. -0.00032 4. 4300 • 5. 12.0900 6. 0.00003200 • 7. 900001 8. 2.34 x 104 • 9. -0.000212000 10. 4002000 _

12. Mathematical Operations with Significant Figures

13. When completing math calculation, the final answer must be reported rounded to the appropriate number of significant figures. • The answer is rounded according to the LAST mathematical operation completed.

14. Rules • 1. Complete calculations following the order of operations. • 2. If the FINAL step is MULTIPLICATION or DIVISION: • A. Look at each value given in the problem and find the one with the LEAST number of significant figures. • B. Round the FINAL ANSWER to the same number of significant figures. • DO NOT ROUND UNTIL THE FINAL STEP!

15. Mult/Div Examples • 4.59 X 1.22 = 5.5998 = 5.5998 =5.60 • 3 sf 3sf 3sf 3sf • 3 sf 45.6 = 18581.90709 • 4 sf 0.002454 • = 18587.90709 3sf • = 186003sf

16. ADD/SUBTRACT • Complete calculations following order of operations. • If the FINAL step is addition or subtraction: • A. Only consider digits to the RIGHT of the decimal. • B. Determine the fewest SF to the right of the decimal. • C. Round final answer to this number of SF.

17. ADD/SUBTRACT EXAMPLES 25.4 (1 sf) 15.000 – 2.3791 = 12.6209 63.66 (2 sf)(3 sf)(4 sf) = 12.621 + 102.44(2 sf) 191.50 = 191.5