1. Scientific Measurement
Chapter 2
Scientific Measurement

2. Chapter 2 Goals – Scientific Measurement
Calculate values from measurements using the correct number of significant figures.
List common SI units of measurement and common prefixes used in the SI system.
Distinguish mass, volume, density, and specific gravity from one another.
Evaluate the accuracy of measurements using appropriate methods.

3. Introduction Everyone uses measurements in some form
Deciding how to dress based on the temperature; measuring ingredients for a recipes; construction.
Measurement is also fundamental in the sciences and for understanding scientific concepts
It is important to be able to take good measurements and to decide whether a measurement is good or bad

4. Introduction
In this class we will make measurements and express their values using the International System of Units or the SI system.
All measurements have two parts: a number and a unit.

5. 2.1 The Importance of Measurement
Qualitative versus Quantitative Measurements
Qualitative measurements give results in a descriptive, nonnumeric form; can be influenced by individual perception
Example: This room feels cold.

6. 2.1 The Importance of Measurement
Qualitative versus Quantitative Measurements
Quantitative measurements give results in definite form usually, using numbers; these types of measurements eliminate personal bias by using measuring instruments.
Example: Using a thermometer, I determined that this room is 24°C (~75°F)
Measurements can be no more reliable than the measuring instrument.

7. 2.1 Concept Practice
1. You measure 1 liter of water by filling an empty 2-liter soda bottle half way. How can you improve the accuracy of this measurement?
2. Classify each measurement as qualitative or quantitative.
a. The basketball is brown
b. the diameter of the basketball is 31 centimeters
c. The air pressure in the basketball is 12 lbs/in2
d. The surface of the basketball has indented seams

8. 2.2 Accuracy and Precision
Good measurements in the lab are both correct (accurate) and reproducible (precise)
accuracy – how close a single measurement comes to the actual dimension or true value of whatever is measured
precision – how close several measurements are to the same value
Example: Figure 2.2, page 29 – Dart boards….

9. 2.2 Accuracy and Precision
All measurements made with instruments are really approximations that depend on the quality of the instruments (accuracy) and the skill of the person doing the measurement (precision)
The precision of the instrument depends on the how small the scale is on the device.
The finer the scale the more precise the instrument.
2.2 Demo, page 28

10. 2.2 Concept Practice
3. Which of these synonyms or characteristics apply to the concept of accuracy? Which apply to the concept of precision?
a. multiple measurements
b. correct
c. repeatable
d. reproducible
e. single measurement
f. true value

11. 2.2 Concept Practice
4. Under what circumstances could a series of measurements of the same quantity be precise but inaccurate?

12. 2.3 Scientific Notation
In chemistry, you will often encounter numbers that are very large or very small
One atom of gold = g
One gram of H = 301,000,000,000,000,000,000,000 H molecules
Writing and using numbers this large or small is calculations can be difficult
It is easier to work with these numbers by writing them in exponential or scientific notation

13. 2.3 Scientific Notation
scientific notation – a number is written as the product of two numbers: a coefficient and a power of ten
Example: 36,000 is written in scientific notation as 3.6 x 104 or 3.6e4
Coefficient = 3.6 → a number greater than or equal to 1 and less than 10.
Power of ten / exponent = 4
3.6 x 104 = 3.6 x 10 x 10 x 10 x 10 = 36,000

14. 2.3 Scientific Notation
When writing numbers greater than ten in scientific notation the exponent is positive and equal to the number of places that the exponent has been moved to the left.

15. 2.3 Scientific Notation
Numbers less than one have a negative exponent when written in scientific notation.
Example: is written in scientific notation as 8.1 x 10-3
8.1 x 10-3 = 8.1/(10 x 10 x 10) =
When writing a number less than one in scientific notation, the value of the exponent equals the number of places you move the decimal to the right.

16. 2.3 Scientific Notation
To multiply numbers written in scientific notation, multiply the coefficients and add the exponents.
(3 x 104) x (2 x 102) = (3 x 2) x = 6 x 106
To divide numbers written in scientific notation, divide the coefficients and subtract the exponent in the denominator (bottom) from the exponent in the numerator (top).
(6 x 103)/(2 x 102) = (6/2) x = 3 x 101

17. 2.3 Scientific Notation
Before numbers written in scientific notation are added or subtracted, the exponents must be made the same (as a part of aligning the decimal points).
(5.4 x 103)+(6 x 102) = (5.4 x 103)+(0.6 x 103)
= ( ) x 103 = 6.0 x 103

18. 2.3 Concept Practice
5. Write the two measurements given in the first paragraph of this section in scientific notation.
a. mass of a gold atom = g
b. molecules of hydrogen =
301,000,000,000,000,000,000,000 H molecules

19. 2.3 Concept Practice
6. Write these measurements in scientific notation. The abbreviation m stands for meter, a unit of length.
a. The length of a football field, 91.4 m
b. The diameter of a carbon atom, m
c. The radius of the Earth, 6,378,000 m
d. The diameter of a human hair, m
e. The average distance between the centers of the sun and the Earth, 149,600,000,000 m

20. 2.4 Significant Figures in Measurement
The significant figures in a measurement include all the digits that are known precisely plus one last digit that is estimated.
Example: With a thermometer that has 1° intervals, you may determine that the temperature is between 24°C and 25°C and estimate it to be 24.3°C.
You know the first two digits (2 and 4) with certainty, and the third digit (3) is a “best guest”
By estimating the last digit, you get additional information

21. Rules 1. Every nonzero digit in a recorded measurement is significant.
- Example: 24.7 m, m, and 714 m all have three sig. figs.
2. Zeros appearing between nonzero digits are significant.
- Example: 7003 m, m, and m all have 4 sig. figs.

22. Rules
3. Zeros appearing in front of all nonzero digits are not significant; they act as placeholders and cannot arbitrarily be dropped (you can get rid of them by writing the number in scientific notation).
- Example: m has two sig. figs. And can be written as 7.1 x 10-3
4. Zeros at the end of the number and to the right of a decimal point are always significant.
- Example: m, m, and all have 4 sig. figs.

23. Rules
5. Zeros at the end of a measurement and to the left of the decimal point are not significant unless they are measured values (then they are significant). Numbers can be written in scientific notation to remove ambiguity.
- Example: 7000 m has 1 sig. fig.; if those zeros were measured it could be written as x 103

24. Rules
6. Measurements have an unlimited number of significant figures when they are counted or if they are exactly defined quantities.
- Example: 23 people or 60 minutes = 1 hour
* You must recognize exact values to round of answers correctly in calculations involving measurements.

25. Significant Figures – Example 1
How many significant figures are in each of the following measurements?
a. 123 m
b cm
c mm
d x 104 m
e m
f. 22 meter sticks
g m
h m

26. 2.4 Concept Practice
7. Write each measurement in scientific notation and determine the number of significant figures in each.
a m
b dm
c mm
d. 12 basketball players
e km
f. 507 thumbtacks

27. Significant Figures in Calculations
The number of significant figures in a measurement refers to the precision of a measurement; an answer cannot be more precise than the least precise measurement from which it was calculated.
Example: The area of a room that measures 7.7 m (2 sig. figs.) by 5.4 m (2 sig. figs.) is calculated to be m2 (4 sig. figs.) – you must round the answer to 42 m2

28. Rounding – The Rule of 5
If the digit to the right of the last sig. fig is less than 5, all the digits after the last sig. fig. are dropped.
Example: m rounds to m (for 4 sig. figs.)
If the digit to the right is 5 or greater, the value of the last sig. fig. is increased by 1.
Example: m rounds to m (for 4 sig. figs.)

29. Rounding – Example 2

30. Addition and Subtraction
The answer to an addition or subtraction problem should be rounded to have the same number of decimal places as the measurement with the least number of decimal places.

31. Multiplication and Division
In calculations involving multiplication and division, the answer is rounded off to the number of significant figures in the least precise term (least number of sig. figs.) in the calculations

32. 2.6 SI Units
The International System of Units, SI, is a revised version of the metric system
Correct units along with numerical values are critical when communicating measurements.
The are seven base SI units (Table 2.1) of which other SI units are derived.
Sometimes non-SI units are preferred for convenience or practical reasons

33. 2.6 SI Units – Table 2.2 Quantity SI Base or Derived Unit Non-SI Unit
Length
meter (m)
Volume
cubic meter (m3)
liter
Mass
kilogram (kg)
Density
grams per cubic centimeter (g/cm3); grams per mililiter (g/mL)
Temperature
kelvin (K)
degree Celcius (°C)
Time
second (s)
Pressure
Pascal (Pa)
atmosphere (atm); milimeter of mercury (mm Hg)
Energy
joule (J)
calorie (cal)

34. Common SI Prefixes Units larger than the base unit Tera T
terameter (Tm)
Giga G
e-9 =
gigameter (Gm)
Mega M
e-6 =
megameter (Mm)
Kilo k
e-3 = 0.001
kilometer (km)
Hecto h
e-2 = 0.01
hectometer (hm)
Deka da
e-1 = 0.1
decameter (dam)
Base Unit
e0 = 1
meter (m)

35. Common SI Prefixes Units smaller than the base unit e0 = 1 meter (m)
Deci d
e1 = 10
decimeter (dm)
Centi c
e2 = 100
centimeter (cm)
Milli m
e3 = 1000
millimeter (mm)
Micro μ
e6 = 1,000,000
micrometer (μm)
Nano n
e9 = 1,000,000,000
Nanometer (nm)
Pico p
e12 = 1,000,000,000,000
picometer (pm)

36. Common SI Prefixes
A mnemonic device can be used to memorize these common prefixes in the correct order:
The Great Monarch King Henry Died By Drinking Chocolate Mocha Milk Not Pilsner

37. 2.7 Units of Length The basic unit of length is the meter
Prefixes can be used with the base unit to more easily represent small or large measurements
Example: A hyphen (12 point font) measures about m or 1 mm.
Example: A marathon race is approximately
42,000 m or 42 km.

38. 2.7 Concept Practice
15. Use the tables in the text to order these lengths from smallest to largest.
a. centimeter
b. micrometer
c. kilometer
d. millimeter
e. meter
f. decimeter

39. 2.8 Units of Volume
The space occupied by any sample of matter is called its volume
The volume of rectangular solids can be calculated by multiplying the length by width by height
Units are cubed because you are measuring in 3 dimensions
Volume of liquids can be measured with a graduated cylinder, a pipet, a buret, or a volumetric flask

40. 2.8 Units of Volume
A convenient unit of measurement for volume in everyday use is the liter (L)
Milliliters (mL) are commonly used for smaller volume measurements and liters (L) for larger measurements
1 mL = 1 cm3
10 cm x 10 cm x 10 cm = 1000 cm3 = 1 L

41. 2.8 Units of Volume

42. 2.8 Concept Practice
17. From what unit is a measure of volume derived?

43. 2.8 Practice
18. What is the volume of a paperback book 21 cm tall, 12 cm wide, and 3.5 cm thick?
19. What is the volume of a glass cylinder with an inside diameter of 6.0 cm and a height of 28 cm?
V=πr2h

44. 2.9 Units of Mass
A person on the moon would weigh 1/6 of his/her weight on Earth.
This is because the force of gravity on the moon is approximately 1/6 of its force of Earth.
Weight is a force – it is a measure of the pull on a given mass by gravity; it can change by location.
Mass is the quantity of matter an object contains
Mass remains constant regardless of location.
Mass v. Weight

45. 2.9 Units of Mass The kilogram is the basic SI unit of mass
It is defined as the mass of 1 L of water at 4°C.
A gram, which is a more commonly used unit of mass, is 1/1000 of a kilogram
1 gram = the mass of 1 cm3 of water at 4°C.

46. 2.9 Concept Practice
20. As you climbed a mountain and the force of gravity decreased, would your weight increase, decrease, or remain constant? How would your mass change? Explain.
21. How many grams are in each of these quantities?
a. 1 cg b. 1 μg c. 1 kg d. 1mg

47. 2.10 Density
Density is the ratio of the mass of an object to its volume.
Equation → D = mass/volume
Common units: g/cm3 or g/mL
Example: 10.0 cm3 of lead has a mass 114 g
Density (of lead) = 114 g / 10.0 cm3 = 11.4 g/cm3
See Table 2.7, page 46

48. 2.10 Density
Density determines if an object will float in a fluid substance.
Examples: Ice in water; hot air rises
Density can be used to identify substances
See Table 2.8, page 46

49. 2.10 Concept Practice
22. The density of silver is 10.5 g/cm3 at 20°C. What happens to the density of a 68-g bar of silver that is cut in half?

50. 2.10 Concept Practice
23. A student finds a shiny piece of metal that she thinks is aluminum. In the lab, she determines that the metal has a volume of 245 cm3 and a mass of 612 g. Is the metal aluminum?
24. A plastic ball with a volume of 19.7 cm3 has a mass of 15.8 g. Would this ball sink or float in a container of gasoline?

51. 2.10 Specific Gravity (Relative Density)
Specific gravity is a comparison of the density of a substance to the density of a reference substance, usually at the same temperature.
Water at 4°C, which has a density of 1 g/cm3, is commonly used as a reference substance.
Specific gravity = density of substance (g/cm3)
density of water (g/cm3)
Because units cancel, a measurement of specific gravity has no units
A hydrometer can be used to measure the specific gravity of a liquid.

52. 2.11 Concept Practice
25. Why doesn’t a measurement of specific gravity have a unit?
26. Use the values in Table 2.8 to calculate the specific gravity of the following substances.
a. Aluminum b. Mercury c. ice

53. 2.12 Measuring Temperature
Temperature determines the direction of heat transfer between two objects in contact with each other.
Heat moves from the object at the higher temperature to the object at a lower temperature.
Temperature is a measure of the degree of hotness or coldness of an object.
Almost all substances expand with an increase in temperature and contract with a decrease in temperature
An important exception is water

54. 2.12 Measuring Temperature
There are various temperature scales
On the Celsius temperature scale the freezing point of water is taken as 0°C and the boiling point of water at 100°C

55. 2.12 Measuring Temperature
The Kelvin scale (or absolute scale) is another temperature scale that is used
On the Kelvin scale the freezing point of water is
273 K and the boiling point is 373 K (degrees are not used).
1°C = 1 Kelvin
The zero point (0 K) on the Kelvin scale is called absolute zero and is equal to -273°C
Absolute zero is where all molecular motion stops

56. 2.12 Measuring Temperature
Converting Temperatures:
K = °C + 273
°C = K - 273

57. 2.12 Concept Practice
27. Surgical Instruments may be sterilized by heating at 170°C for 1.5 hours. Convert 170°C to kelvins.
28. The boiling point of the element argon is 87 K. What is the boiling point of argon in °C?

58. 2.13 Evaluating Measurements
Accuracy in measurement depends on the quality of the measuring instrument and the skill of the person using the instrument.
Errors in measurement could have various causes
In order to evaluate the accuracy of a measurement, you must be able to compare it to the true or accepted value.

59. 2.13 Evaluating Measurements
accepted value – the true or correct value based or reliable references
experimental value – the measured value determined in the experiment
The difference between the accepted value and the experimental value is the error.
error = accepted value – experimental value

60. 2.13 Evaluating Measurements
The percent error is the error divided by the accepted value, expressed as a percentage of the accepted value.
Percent Error = x 100
An error can be positive or negative, but an absolute value of error is used so that the percentage is positive
|error| AV

61. 2.13 Concept Practice
32. A student estimated the volume of a liquid in a beaker as 208 mL. When she poured the liquid into a graduated cylinder she measured the value as 200 mL. What is the percent error of the estimated volume from the beaker, taking the graduated cylinder measurement as the accepted value?