BELL%20RINGER%20

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 cylinders 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 125.45 5648 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
• 18600 3sf

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