1. Scientific Measurement
Chapter 3

2. Measurement & Uncertainty
Making measurements and performing calculations with measurements is very important in science and many other fields
Any measurement has a number with a unit
How do you know if a measurement is true?
Are there limits to measurement?

3. Scientific Notation
A convenient way of writing very large and very small numbers
A way to indicate significant figures
Standard (Decimal) notation
m (radius of H atom)
Scientific notation
3.0 x m
coefficient x 10 power
first digit must be from 1 to 9
1.65 x Correct format?
0.053 x Correct format?
12.63 x Correct format?

4. Calculations with Scientific Notation
Review scientific notation in your text
Read pages R56-57, Appendix C
Your calculator uses a special key to enter scientific notation
EE, E, Exp, Sci
These keys mean “x 10exp” to your calculator
Do not use 10^

5. Calculations with Scientific Notation
How to enter x 1023
6.022
2nd EE 23
Your calculator screen should show 6.022E23

6. Calculations with Scientific Notation
Calculate 6.52 x 1018 ÷ 4.91 x 10-5
6.52
2nd EE 18 ÷
4.91 -5
ENTER = 1.33…..E23

7. Accuracy, Precision, & Error
Accuracy and precision are not the same thing
Accuracy
how close a measurement is to the true value (actual or accepted value)
Precision
how close measurements agree
how exact a measurement is
Example: a centigram balance (0.01g) is more precise than a decigram balance (0.1g)
Error
difference between actual and experimental value

8. Accuracy & Precision

9. Accuracy & Precision To evaluate accuracy of a measurement:
compare measurement to true value
To evaluate precision of a measurement:
compare values of two or more repeated measurements

10. Uncertainty in Measurement
All measurements are approximations
All measurements contain error, so we can only report numbers that we know for sure (certain)
The certainty of a measurement is determined by the precision of the measurement
Significant figures are used to reflect certainty of measured value

11. Uncertainty in Measurement
Digital instruments (like our electronic scales) estimate the final digit
Example: g
In this measurement, the 7 is estimated by the scale
The uncertainty of the scale is the smallest division reported by the scale (0.01 g)
Recording the measurement with its uncertainty: ± 0.01 g

12. Significant Figures
All digits that are known, plus one last estimated digit
Represent certainty of a measurement
Must be handled properly in calculations to prevent overstating precision
Review rules to determine significant figures (p )

13. Significant Figures in Measurement

14. Rules for Determining Significant Figures
All non-zeros YES
Zeros between non-zeros YES
Zeros at the beginning of a # NO
Zeros at the end, to right of “.” YES
Final zeros without “.” NO
Final zeros with “.” YES

15. Significant Figures in Calculations
Multiplication & Division
Result must have the same # of s.f. as the measurement with the fewest s.f.
6.221 cm x 5.2 cm = cm2 → 32 cm2
Addition & Subtraction
Result may not have more decimal places than the number with the fewest decimal places
= → 105

16. Uncertainty in Measurement
An error due to limitations of the instrument
For a digital instrument
+/- the smallest digit
62.56g +/ g
For an analog instrument
+/- the estimated digit
See example

17. Determining Error Error:
the difference between the accepted and experimental measurement
Example:
Water was measured to boil at 101.5ºC
The known bp of water is 100.0ºC
Calculate the error in the measurement

18. Percent Error
Error is often better understood as a percent of the true value
Note that the numerator is absolute value!

19. 3.2 International System of Units
SI units (System International) used to be called the metric system
Standard units used in science

20. Metric Prefixes*
*Memorize these prefixes and their factors

21. Common Units of Volume

22. Mass vs. Weight Mass is a measure of matter
Anything that occupies space has mass
Weight is a force
The force of gravity acting on a mass

23. Temperature Scales Used in Science
Kelvin (Absolute Temperature)
Absolute zero 0º K = º C
no negative temps
Celsius
0 C = K
A Kelvin degree and a Celsius degree have the same size

24. Conversions Between the Celsius and Kelvin Scales
We will not use the Farenheit scale!

26. Energy
Units of Energy
Energy is the capacity to do work or to produce heat.
The joule (J) is the SI unit of energy.
One calorie (cal) is the quantity of heat that raises the temperature of 1 g of pure water by 1°C.

27. The Joule Pronunciation GuideNO NO
YES!

28. Energy can be converted into other forms, but the units are still joules (J)
This house is equipped with solar panels. The solar panels convert the radiant energy from the sun into electrical energy that can be used to heat water and power appliances.

29. 3.3 Conversion Problems Conversion Factors
Ratio of two equivalent measurements
1 dozen = 12 items

30. Dimensional Analysis When solving problems, units must be consistent
Unit conversion are often necessary
Use conversion factors
Problem: Determine how many centimeters are in 1 yd.
1 yd x in x 2.54 cm = cm
1 yd in

31. 3.4 Density Density is the ratio of mass to volume
Density is an intensive property
Density of a pure substance is constant at a given temperature

32. Density Depends on temperature Units temp  density
What if temp decreased?
Units
g/cm3 or g/mL for solids & liquids
g/L for gases