Transcript Significant Figures Power Point 9-18-13
Significant Figures
Dealing with uncertainty in measurements.
What values are shown below?
• 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.
• 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.
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?
Rules for Significant Figures
• 1. ALL NON-ZERO digits are considered significant. • Examples 125.45 5648 1.1211
• 2. Zeros BETWEEN NON-ZERO DIGITS are SIGNIFICANT parts of a measurement.
• Examples 5005 120301
• 3. Zeros BOTH TO THE RIGHT OF a non-zero digit AND a WRITTEN DECIMAL are significant.
• Examples 124.000 5.000
• 4. Zeros that SERVE ONLY AS PLACEHOLDERS are NOT SIGNIFICANT .
• Examples 0.000003432 0.0021111
• 5 . Zeros to THE RIGHT OF A NON-ZERO DIGIT BUT to the LEFT OF AN UNDERSTOOD DECIMAL are NOT SIGNIFICANT …..they can be the RESULT OF ROUNDING OFF !
• If a BAR is placed ABOVE A ZERO it makes ALL digits OVER TO AND INCLUDING THE ZERO WITH THE BAR SIGNIFICANT.
_ • Example 3400 1250000 •
NOTE
– If the number is in SCIENTIFIC NOTATION consider the COEFFICIENT when determining SFs.
only
Practice Problems
• Determine how many figures are significant in each of these measurements: • 1. 375 • 3. -0.00032
2. 89.000
4. 4300 • 5. 12.0900
6. 0.00003200
• 7. 900001 8. 2.34 x 10 4 _ • 9. -0.000212000 10. 4002000
Mathematical Operations with Significant Figures
• 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.
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!
Mult/Div Examples
• 4.59 X 1.22 = 5.5998 = 5.59
98 = 5.60
• 3 sf 3sf 3sf 3sf • • • 3 sf • 4 sf 45.6 0.002454
= 18581.90709
= 185 87.90709 3sf = 18600 3sf
ADD/SUBTRACT
• Complete calculations following order of operations.
• If the FINAL step is addition or subtraction: – A. Only consider digits to the
RIGHT
decimal.
of the – B. Determine the fewest SF to the right of the decimal.
– C. Round final answer to this number of SF.
ADD/SUBTRACT EXAMPLES
25.4 (1 sf) 63.66 (2 sf) + 102.44
(2 sf) 191.5
0 = 191.5
15.000 – 2.3791 = 12.620
9 (3 sf) (4 sf) = 12.621