1. Using Scientific Measurements
Section 2.3

2. Accuracy and Precision
Accuracy refers to the closeness of measurements to the correct or accepted value of the quantity measured.
Precision refers to the closeness of a set of measurements of the same quantity made in the same way.

5. A measurement was taken three times. The correct measurement was 68
A measurement was taken three times. The correct measurement was 68.1 mL.  Circle whether the set of measurements is accurate, precise, both, or neither.
mL, 43.9 mL, 2.0 mL                              accurate       precise       both       neither
mL, 68.2 mL, 68.0 mL                            accurate       precise       both       neither
mL, 98.2 mL, 97.9 mL                            accurate       precise       both       neither

6. Percent Error
The accuracy of an individual value or of an average experimental value can be compared quantitatively with the correct or accepted value by calculating the percentage error.

7. Sample problem
 A student measures the mass and volume of a substance and calculated its density as 1.40 g/mL. The corret or accepted value of the density is g/mL. What is the percentage error of the student's measurement?

8. Error in Measurement
Every experimental measurement has a degree of uncertainty.
The volume, at the right is certain in the 10’s place, Greater than 10ml and less than 20ml
The 1’s digit is also certain, greater than 17ml and less than 20ml.
A best guess is needed for the tenths place.

9. Precision and Instruments
Do all measuring devices have the same amount of precision?

10. Ex: The scale on the left has an uncertainty of (+/- .1g)
You indicate the precision of the equipment by recording its Uncertainty
Ex:  The scale on the left has an uncertainty of (+/- .1g)
Ex:  The scale on the right has an uncertainty of   (+/- .01g)

13. Significant Figures
In Science, measured values are reported in terms of significant figures.
Significant figures in a measurement include all of the known digits plus one estimated digit.

14. For example… Look at the ruler below Each line is 0.1cm
You can read that the arrow is on 13.3 cm
However, using significant figures, you must estimate the next digit
That would give you cm

15. Let’s try this one Look at the ruler below
What can you read before you estimate?
12.8 cm
Now estimate the next digit…
12.85 cm

16. Rules for Determining Significant Zeros
How many significant digits are in the following numbers?
274
25.632
8.988
Rule #1
All non zero digits are ALWAYS significant

17. Rules for Determining Significant Zeros
How many significant digits are in the following numbers?
507
60007
9.088
Rules for Determining Significant Zeros
Rule #2.
All zeros between significant digits are ALWAYS significant

18. Rules for Determining Significant Zeros
How many significant digits are in the following numbers?
32.0
19.000
Rules for Determining Significant Zeros
Rule #3
All FINAL zeros to the right of the decimal ARE significant

19. Rules for Determining Significant Zeros
How many significant digits are in the following numbers
0.0002
Rules for Determining Significant Zeros
Rule #4
All zeros that act as place holders are NOT significant
Another way to say this is: zeros are only significant if they are between significant digits OR are the very final thing at the end of a decimal.

20. Determine the number of significant figures in each of the following.km
1002 m
400 mL Cm kg

21. B) 4 significant figures C) 6 significant figures
Suppose the value "seven thousand centimeters" is reported to you. How should the number be expressed if it is intended to contain the following?
A) 1 significant figure
B) 4 significant figures
C) 6 significant figures

22. Do Now How many significant figures are in each of the following measurements?
A) mL SF
B) 6000 g ~4 SF
C) km 6 SF
D) 400. mm 3 SF

23. Rules for Rounding numbers # 1
•If the digit to the immediate right of the last significant digit is greater than 5, you round up the last significant figure
•Let’s say you have the number and you want 4 significant digits
• – The last number you want is the 8 and the number to the right is a 7
•Therefore, you would round up & get 234.9

24. Rules for Rounding numbers # 2
•If the digit to the immediate right of the last significant digit is less than 5, do not round up the last significant digit.
•For example, let’s say you have the number and you want 3 significant digits
•The last number that you want is the 8 – 43.82
•The number to the right of the 8 is a 2
•Therefore, you would not round up & the number would be 43.8

25. Rules for Rounding numbers # 3
•If the number to the immediate right of the last significant is a 5, and that 5 is followed by a non zero digit, round up
•78.657  (you want 3 significant digits)
•The number you want is the 6
•The 6 is followed by a 5 and the 5 is followed by a non zero number
•Therefore, you round up
•78.7

26. Rules for Rounding numbers # 4
•If the number to the immediate right of the last significant is a 5, and that 5 is followed by a zero, you look at the last significant digit and make it even.
•2.5350  (want 3 significant digits)
•The number to the right of the digit you want is a 5 followed by a 0
•Therefore you want the final digit to be even
•2.54

27. Rules for Rounding numbers # 5
•2.5250    (want 3 significant digits)
•The number to the right of the digit you want is a 5 and it is not follow by a non-zero digit , and the preceding digit is even the last digit stays the same
•2.52

28. Addition or Substraction with significant figures
When adding or subtracting decimals, the answer must have the same number of digits to the right of the decimal point as there are in the measurement having the fewest digits to the right of the decimal point.
2.03 g+25.1g= 27.13g        27.1g
When working with whole numbers the answer should be rounded so that the final significant digit is in the same place as the leftmost uncertain digit.
= 5800

29. Multiplication or substraction with significant figures
The answer can have no more significant figures than are in the measurement with the fewest number of significant figures.
3.05 g/ 8.47 g = g           0.360g

30. Practice Problems What is the sum of 2.009 g and 0.05681 g ?
Calculate the quantity 87.3 cm – cm.
Calculate the area of a rectangular crystal surface that measures 1.34 µm by µm (Area= length x with)
Polycarbonate plastic has a density of 1.2 g/cm³. a photo frame is constructed from two 3.0 mm sheets of polycarbonate. Each sheet measures 28 cm by 22 cm. what is the mass of the photo frame?