1. Accuracy, Precision, & Significant Digits
Chemistry CP
Accuracy, Precision, & Significant Digits

2. Objectives Define accuracy Define precision
Compare accuracy & precision
Use significant figures

3. Accuracy
Accuracy refers to how closely a measurement matches the true or actual values
To be accurate only requires the true value (bulls eye) & one measurement (for the arrow to hit the target)
Highly accurate data can be costly and difficult to acquire

4. Precision
Precision refers to the reproducibility of the measurement and exactness of description in a number.
To decide on precision, you need several measurements (notice multiple arrow holes), and you do not need to know the true value (none of the values are close to the target but all the holes are close together.)

5. Accuracy & Precision
In order to be accurate and precise, one must pay close attention to detail to receive the same results every time as well as “hit the target”.

6. Comparing Accuracy & Precision
Notice the difference in these pictures.
To win the tournament the archers must hit the target the most times. The winner must show accuracy & precision.
The 1st archer has _____ accuracy & ____ precision.
The 2nd archer has _____ accuracy & ____ precision.
The 3rd archer has _____ accuracy & ____ precision.
The 4th archer has _____ accuracy & _____ precision
BAD
BAD
BAD
GOOD
GOOD
GOOD
GOOD
BAD

7. Example 1
A sample is known to weigh g. Jane weighed the sample five different times with the resulting data. Which measurement was the most accurate?
3.200 g
3.180 g
3.152 g
3.189 g

8. Example 2
Consider the data (in cm) for the length of an object as measured by three students. The length is known to be 14.5 cm. Which student had the most precise work, and which student had the most accurate work?
Trial 1
Trial 2
Trial 3
Trial 4
Trial 5
Student A
14.8
14.7
Student B
14.2
14.6
Student C
14.4
14.5

9. Solution
Most precise: Student C and A have same percision (0.1 cm difference)
Most accurate: Student C (2 were true value, rest within 0.1 cm)
Trial 1
Trial 2
Trial 3
Trial 4
Trial 5
Student A
14.8
14.7
Student B
14.2
14.6
Student C
14.4
14.5

11. Significant Figures Why are significant figures necessary?
True accuracy is no better than the measurement obtained by the least precise method.
We use significant digits so we are not exaggerating our precision.

12. Rules of Significant Digits
All digits 1 through 9 are significant.
9.342 mg = 4 Sig. Digits
233,124 = 6 sig. digits

13. Rules of Significant Digits
2. Zero is significant when it is between two non‐zero digits
= 3 SD
206 = 3 SD
100,001 = 6 SD

14. Rules of Significant Digits
3. A zero to the right of a decimal point in a number greater than or equal to one is significant.
(4 SD)
(4 SD)
(4 SD)
(6 SD)
(3 SD)

15. Rules of Significant Digits
4. A zero to the right of a decimal point (in a number less than one) but to the left of nonzero digit is not significant.
(4 SD)
(5 SD)

16. Rules of Significant Digits
5. Zeros used only to space the decimal point (placeholders) are not significant (1 SD) (3 SD) -78,000 (2 SD)

17. Counting SDs How many significant digits are in the following numbers?
1235
2020
235.0
0.0270
235
65,100
19,620,000,000
102, 800

18. Estimated to the tens place Estimated to the tenths place
Why are S.F.s Important?
When reporting a measurement the number of digits indicates the precision of an instrument.
100 ml
Estimated to the tens place
99.9 mL
Estimated to the tenths place

19. Why are S.F.s Necessary? When you divide 5.0 /0.87 = 5.7471…
(Actual Answer: 5.7)
S.F.s will provide a way to determine how many numbers to report in a measurement or calcualtion!

20. Example 1:
How would you record this measurement?
1.37 cm

21. Example 2: Provide the measurements for each example.B.

22. How many significant digits would be recorded?10 20 30 40 50 60 70 B. 10 20 30 40 50 60 70 C. 10 20 30 40 50 60 70

23. How many significant digits would be recorded?
48 cm (2 sfs) A. 10 20 30 40 50 60 70 B.
48 cm (2 sfs) 10 20 30 40 50 60 70 C.
48.0 cm (3 sfs) 10 20 30 40 50 60 70