1. Accuracy, Precision, & Significant Figures
Chapter 1, Section 4

2. Accuracy and Precision
How close you are to the actual value
Depends on the person measuring
Calculated by the formula:
Precision:
How finely tuned your measurements are or how close they can be to each other
Depends on the measuring tool
Determined by the number of significant digits

3. Accuracy and Precision
Accuracy & Precision may be demonstrated by shooting at a target.
Accuracy is represented by hitting the bulls eye (the accepted value)
Precision is represented by a tight grouping of shots (they are finely tuned)

5. Precision and Significant Figures
The precision of a measurement is the smallest possible unit that could be measured.
Significant Digits (sd) are the numbers that result from a measurement.
When a measurement is converted we need to make sure we know which digits are significant and keep them in our conversion
All digits that are measured are significant

6. What is a significant figure?
There are 2 kinds of numbers:
Exact: the amount of money in your account. Known with certainty.

7. What is a significant figure?
Approximate: weight, height—anything MEASURED. No measurement is perfect.

8. When to use Significant figures
When a measurement is recorded only those digits that are dependable are written down.

9. When to use Significant figures
If you measured the width of a paper with your ruler you might record 21.7cm.
To a mathematician 21.70, or is the same.

10. But, to a scientist 21.7cm and 21.70cm is NOT the same
21.700cm to a scientist means the measurement is accurate to within one thousandth of a cm.

11. But, to a scientist 21.7cm and 21.70cm is NOT the same
If you used an ordinary ruler, the smallest marking is the mm, so your measurement has to be recorded as 21.7cm.

12. How do I know how many Sig Figs?
Rule: All digits are significant starting with the first non-zero digit on the left.

13. How do I know how many Sig Figs?
Exception to rule: In whole numbers that end in zero, the zeros at the end are not significant.

14. How many sig figs? 7 40
0.5
7 x 105
7,000,000 1

15. How do I know how many Sig Figs?
2nd Exception to rule: If zeros are sandwiched between non-zero digits, the zeros become significant.

16. How do I know how many Sig Figs?
3rd Exception to rule: If zeros are at the end of a number that has a decimal, the zeros are significant.

17. How do I know how many Sig Figs?
3rd Exception to rule: These zeros are showing how accurate the measurement or calculation are.

18. How many sig figs here?
1.2
2100
56.76
4.00
0.0792
7,083,000,000 2 4 3

19. How many sig figs here?
3401
2100
2100.0
5.00
8,000,050,000 4 2 5 3 6

20. What about calculations with sig figs?
Rule: When adding or subtracting measured numbers, the answer can have no more places after the decimal than the LEAST of the measured numbers.

21. Add/Subtract examples
2.45cm + 1.2cm = 3.65cm,
Round off to = 3.7cm
7.432cm + 2cm = round to  9cm

22. Multiplication and Division
Rule: When multiplying or dividing, the result can have no more significant figures than the least reliable measurement.

23. A couple of examples 75.8cm x 9.6cm = ?
56.78 cm x 2.45cm = cm2
Round to  139cm2
75.8cm x 9.6cm = ?

24. Have Fun Measuring and Happy Calculating!
The End
Have Fun Measuring and Happy Calculating!