1. Lecture 5 Significant Figures Ozgur Unal
NIS – CHEMISTRY
Lecture 5
Significant Figures
Ozgur Unal

2. NIS – CHEMISTRY Lesson Objectives:
Define accuracy, precision and error.
Compare and contrast accuracy and precision.
State the rules of writing significant figures.

3. Uncertainty in Data Accuracy vs Precision:
Accuracy refers to how close a measured value is to an accepted value.
Precision refers to how close a
series of measurements are to
one another.

4. Accuracy vs Precision
Table below shows the density of an object measured by 3 students in 3 trials.
The accepted value for the density of the object is 1.59 g/cm^3.
Which student has the most accurate data?
Which student has the most precise data?
StudentA
Student B
Student C
Density
Error
Trial 1
1.54
-0.05
1.40
-0.19
1.70
+0.11
Trial 2
1.60
+0.01
1.68
+0.09
1.69
+0.10
Trial 3
1.57
-0.02
1.45
-0.14
1.71
+0.12
Student A has the most accurate, student C has the most precise data.

5. Error and Percent Error
Error is defined as the difference between the experimental value and an accepted value.
StudentA
Student B
Student C
Density
Error
Trial 1
1.54
-0.05
1.40
-0.19
1.70
+0.11
Trial 2
1.60
+0.01
1.68
+0.09
1.69
+0.10
Trial 3
1.57
-0.02
1.45
-0.14
1.71
+0.12
Percent error expresses error as a percentage of the accepted value.
percent error = 100*|error| / accepted value

6. Significant Figures
Precision is limited by the tools available, i.e. your ruler.
Accurate and presice measurements rely on the skill of the person using the instrument.
The precision of a measurement is indicated by the number of digits reported.
Significant figures include all known digits plus one estimated digit.
Measure the length of your eraser..

7. Significant Figures
Five rules for recognizing the significant figures in a number:
Nonzero numbers are always significant has 3 sig. fig.
Zeroes between nonzero numbers are always significant has 4 sig. fig.
All final zeroes to the right of the decimal are significant has 3 sig. fig.
Placeholder zeroes are not significant. To remove placeolder zeroes, rewrite the number in scientific notation has 3 sig. fig.
Counting numbers and defined constants have an infinite number of significant figures. 6 molecules has infinite number of sig. fig.

8. Significant Figures - Exercises
341
 3 significant figures
0.019
 2 significant figures
60,086
 5 significant figures
 3 significant figures
19.20
 4 significant figures
270
 2 significant figures

9. Lecture 6 Rounding Numbers Ozgur Unal
NIS – CHEMISTRY
Lecture 6
Rounding Numbers
Ozgur Unal

10. NIS – CHEMISTRY Lesson Objectives:
State the purpose of rounding numbers.
Round off a number to a desired significant figure.
Find the number of significant figures desired after an operation.

11. Significant Figures
In multiplication and division the number of significant digits in an answer should equal the least number of significant digits in any one of the numbers being multiplied, divided etc.
11.3 cm * 6.8 cm = 77 cm^2
When quantities are being added or subtracted, the number of decimal places (not significant digits) in the answer should be the same as the least number of decimal places in any of the numbers being added or subtracted.
3.6 – 0.57 = 3.0

12. Rounding Numbers
Rules for rounding numbers to a desired significant figures:
If the digit to the right of the last significant figure is less than 5 do not change the last significant figure.
If the digit to the right of the last significant figure is greater than 5, round up the last significant figure.
If the digits to the right of the last significant figure are a 5 followed by a nonzero digit, round up the last significant figure.
If the digits to the right of the last significant figure are a 5 followed by 0 or no other number at all, look at the last significant figure. If it is odd, round it up; if it is even do not round up.

13. Significant Figures - Exercises
2.532
2.53
2.536
2.54
2.5351
2.54
2.5350
2.54
2.5250
2.52
Solve example problem 2.8 on page 54