1. Measurements & Calculations
Chapter 2

2. Scientific Notation Section 2.1
Objective: show how very large or very small numbers can be expressed as the product of a number between 1 and 10 AND a power of 10

3. (the number of atoms in a drop of water)
Scientific Numbers
In science, we often encounter very large and very
small numbers. Using scientific numbers makes
working with these numbers easier
5,010,000,000,000,000,000,000
a very large number
(the number of atoms in a drop of water)
a very small number
(mass of a gold atom in grams)

4. Scientific Numbers
RULE 1
As the decimal is moved to the left
The power of 10 increases one
value for each decimal place moved
Any number to the
Zero power = 1
450,000,000 = 450,000,000. x 10 8 2 3 1
450,000,000 = 450,000,000. x 10 8
4.5 x 10

5. Scientific Numbers 0.0000072 = 0.0000072 x 10 -6 -2 -3 -1
RULE 2
As the decimal is moved to the right
The power of 10 decreases one
value for each decimal place moved
Any number to the
Zero power = 1
= x 10 -6 -2 -3 -1
= x 10 -6
7.2 x 10

6. UNITS and MEASUREMENTS OF LENGTH, VOLUME & MASS
Section 2.2 and 2.3
UNITS and MEASUREMENTS OF LENGTH, VOLUME & MASS
Objective: to learn english, metric and SI systems of measurement

7. Measurements of length, volume & mass
Section 2.3
Measurements of length, volume & mass
Objective: understand metric system for measuring length, volume and mass

8. Property English Unit Metric Unit
Fundamental Quantities
Property English Unit Metric Unit
mass slug gram
1.0 slug ,590 g
length foot meter
1.0 ft m
volume quart liter
1.06 qt L

9. Property Metric Unit English Unit
time second second
temperature Kelvin Fahrenheit

10. Significant Figures Section 2.5
Objective: to learn how to determine the number of sig figs

11. Significant Figures All number other then zero are significant
Ex. 23 = 2 sig figs
Leading zeros- zeros that are at the beginning of a number are NEVER significant
Ex 034 = 2 sig figs and = 3 sig figs
Trapped zeros – zeros that are trapped between two other significant figures are ALWAYS significant
Ex 304 = 3 sig figs and = 5 sig figs
Trailing zeros – zeros that are at the end of a number – depends on if there is a decimal point expressed in that number
If there is a decimal point showing in the number then the zeros are significant
Ex 60 = 1 si fig but 60. = 2 sig figs and 60.0 = 3 sig figs
Ex .05 = 1 sig figs
If there is NOT a decimal point showing in the number then the zeros are NOT sinificant

12. Example:
120000

13. Significant Figures 120000 120000. No decimal point Zeros are not
2 sig figs
Zeros are not
significant!
Decimal
Point
All digits including
zeros to the left of
The decimal are
significant.
6 sig figs

14. Significant Figures 1005 123.00 All figures are Significant 4 sig figs
Zeros between
Non zeros are
significant
123.00
All figures are
Significant
5 sig figs
Zero to the
Right of the
Decimal are
significant

15. Zeros to the right of the decimal And to the right of non zero values
Significant Figures
3 sig figs
Zeros to the right of
The decimal with no
Non zero values
Before the decimal
Are not significant
5 sig figs
Zeros to the right of the decimal
And to the right of non zero values
Are significant

16. Significant Figures 1 in = 2.54cm 4 quarts = 1 gallon
Exact equivalences have an unlimited number of
significant figures
1 in = 2.54cm
Therefore in the statement 1 in = 2.54 cm,
Neither the 1 nor the 2.54 limits the number of
Sig figs when used in a calculation
The same is true for:
4 quarts = 1 gallon
100 centimeters = 1 meter
1000 grams = 1 kilograms
and so on !

17. (numbers that were not obtained using measuring
Exact numbers
(numbers that were not obtained using measuring
devices, but determined by counting)
also have an unlimited number of sig figs
Examples:
3 apples
8 molecules
32 students

18. Uncertainty in Measurement
Section 2.4
Uncertainty in Measurement
Objective: to understand how uncertainty in measurement arises
Difference between accuracy and precision

19. Significant Figures
Significant figures are used to distinguish truly measured values from those simply resulting from calculation. Significant figures determine the precision of a measurement. Precision refers to the degree of subdivision of a measurement.
As an example, suppose we were to ask you to measure how tall the school is, you replied “About one hundred meters”. This would be written as 100 with no decimal point included. This is shown with one significant figure the “1”, the zeros don’t count and it tells us that the building is about 100 meters but it could be 95 m or even 104 m. If we continued to inquire and ask you to be more precise, you might re-measure and say “ OK, ninety seven meters. This would be written as 97m. It contains two significant figures, the 9 and the 7. Now we know that you have somewhere between 96.5m and 97.4m. If we continue to ask you to measure even more precise with more precision, may eventually say, “97.2 m”.
THE PRECISION OF YOUR MEASUREMENT IS DICTATED BY THE INSTRUMENT YOU ARE USING TO MEASURE!!!!

20. Precision = Accuracy ACCURACY MEANS HOW CLOSE A MEASUREMENT
IS TO THE TRUE VALUE
PRECISION REFERS TO THE DEGREE OF
SUBBDIVISION OF THE MEASUREMENT
FOR EXAMPLE, IF A ROOM IS 10 FEET LONG AND
YOU MEASURE IT TO BE FT LONG, YOUR
MEASUREMENT IS VERY PRECISE BUT INACCURATE !
MEASUREMENTS SHOULD BE ACCURATE AND AS
PRECISE AS THE MEASURING DEVICE ALLOWS

21. Illustration of accurate vs percise

22. You tell me. What is it?

23. Precision & Measurement
Measurements are always all measured values plus one
approximated value. The pencil is 3.6 cm long.
With more calibration a more
precise measurement is possible
The pencil is 3.64 cm long! 4
The calibration of the instrument
determines measurement precision
Now cm !

24. What is the precision on a ruler?
Follow directions from Mrs McGrath & try to figure it out???
What if your measurement was in cm?
What if your measurement was in mm?

25. Scales and sig figs In our class Write down what the scale says
Most scales are taken to the hundreths place

26. Graduated Cylinders & Thermometers
First – figure out scale
Then – take measurement out to one guess past certainity

27. Section 2.5 continued
Math and Sig Figs

28. Rules for rounding off In calculations:
Round each number to one sig fig:
If the digit is to be removed:
Is less than 5, the preceding digit stays the same
EX rounds to ???? _____________
is equal to or greater then 5, the preceding digit is increased
EX rounds to ???? _____________
In calculations:
carry the extra digits through to the final result AND THEN round off

29. Addition/Subtraction with Sig Figs
Adding and subtracting with significant figures.
The position, not the number, of the significant figures is important in adding and subtracting. For example,
(the last sig fig is in hundredth place (0.01))
(the last sig fig is in ten thousandth (0.0001))
(the answer is rounded off to
the least significant position
hundredths place)

30. The answer is rounded to the position of least significance
Adding & Subtracting Sig Figs
The numbers in
these positions are
not zeros, they are
unknown
123.6 _
Don’t even look at
The 6 to determine
Rounding. Only
Look at the 4
165.9
The answer is rounded to the
position of least significance

31. Multiplying/Dividing with Significant Figures
The result of multiplication or division can have no more sig figs than the term with the least number.
*ex. 9 x 2 = 20 since the 9 has one sig fig and the 2 has one sig fig, the answer 20 must have only one and is written without a decimal to show that fact.
* By contrast, 9.0 x 2.0 = 18 each term has two sig figs and the answer must also have two.
*4.56 x 1.4 = How many sig figs can this answer have?
6.4 (2 sig figs)

32. Dimensional analysis Section 2.6
Objective: learn how to apply dimensional analysis to solve problems

33. NO KING HENRY
You must use dimensional analysis to convert from metric to metric
You must use your brain and logic to do this
K H D b d c m

34. Some Common Metric Prefixes
Prefix Multiplier Example
milli milliliter
centi centimeter
deci decigram
kilo kilometer
micro microgram 6
Mega megabyte 9
Giga gigabyte

35. From the last slide we learned the meaning of some of the common prefixes, BUT we are going to learn to dimensional analysis using the root prefixes and deciding bigger/smaller.

36. Some Common Metric Prefixes
Prefix Multiplier Prefix
milli milli
centi centi
deci deci
kilo kilo
micro micro 6
Mega mega 9
Giga giga

37. Conversions YOU Need to Memorize
Length
1in = 2.54 cm
39.37 in = 1 meter
1 mile = 5280 feet
Mass
1kg = 2.2 lbs
1lb = 454 grams
Volume
1 liter = 1.06qts
1 gallon = 3.79 liters

38. Dimensional Analysis Rules
1.37days = ? minutes
Always start with the known value over the number 1
Always write one number over the other
Always, Always, Always, Always, Always write/include the unit with the number
1.37 days 1

39. Single step examples Equivalence statements 3.6 m = ? ft 6.07 lb = ?kg
4.2 L = ?qt
35.92 cm = ? in
Length
1in = 2.54 cm
39.37 in = 1 meter
1 mile = 5280 feet
Mass
1kg = 2.2 lbs
1lb = 454 grams
Volume
1 liter = 1.06qts
1 gallon = 3.79 liters

40. Double step Exampls Equivalence Statements 56,345 s = ? yrs
98.3 in = ?m
3.2 mi = ?km
Length
1m = yd
2.54 cm = 1 in
1mi = 1760 yd
Mass
1kg = lb
453.6 g = 1lb
Volume
1 L = 1.06qt

41. Temperature Conversions
Section 2.7
Temperature Conversions
Objective: to learn three temperature scales
to convert from one scale to another

42. Temperature – the average kinetic energy in a substance
Boiling points
Fahrenheit 212 F
Celsius 100 C
Kelvin 373 K
Freezing points
Fahrenheit 32 F
Celsius 0 C
Kelvin K
*O Kelvin or Absolute zero: point at which molecular motion stops

43. Temperature Conversion Formulas
Celsius to Kelvin TK = TC + 273
Kelvin to Celsius TC = TK – 273
Celsius to TF = 1.80TC
Fahrenheit
Fahrenheit to TC = TF - 32
Celsius

44. Section 2.8
Density
Objective: to define density and its units

45. Density: the amount of matter present in a given volume of a substance
Units
Formula
Density = g/ml OR g/cm3
Mass = g (grams)
Volume = ml OR cm3
Liquids OR solids
Density = mass/volume
DENSITY of a substance never changes
Ex gold is ALWAYS 19.3g/cm3
Less dense objects “FLOAT” in more dense objects

46. Example calculation
Mercury has a density of 13.6g/ml. What volume of mercury must be taken to obtain 225 grams of the metal?

47. Example calculation: ANSWER
Mercury has a density of 13.6g/ml. What volume of mercury must be taken to obtain 225 grams of the metal?
16.5 mL

48. THE END 