Unit 1 Measurments PPT - TeacherWeb

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					    Unit 1
and Calculations

Measurement – a quantity that has both a
 number and a unit.

• Measurements are fundamental to the experimental

• Units typically used in the sciences are the
  International System of Measurements (SI)
          Scientific Notation

In science, we deal with some very
LARGE numbers:
1 mole = 602000000000000000000000

In science, we deal with some very
SMALL numbers:
Mass of an electron =
0.000000000000000000000000000000091 kg
         Scientific Notation

 Imagine the difficulty of calculating
 the mass of 1 mole of electrons!

0.000000000000000000000000000000091 kg
          x 602000000000000000000000
     Scientific Notation:

A method of representing very large or
  very small numbers in the form:
         M x 10n

      M is a number between 1 and 10
      n is an integer
        2 500 000 000           .
           9 8 7 6 5 4 3 2 1
Step #1: Insert an understood decimal point
Step #2: Decide where the decimal must end
         up so that one number is to its left
Step #3: Count how many places you bounce
         the decimal point
Step #4: Re-write in the form M x 10n
2.5 x   109

 The exponent is the
 number of places we
 moved the decimal.
             1 2 3 4 5

Step #2: Decide where the decimal must end
         up so that one number is to its left
Step #3: Count how many places you bounce
         the decimal point
Step #4: Re-write in the form M x 10n
5.79 x   10 -5

  The exponent is negative
  because the number we
  started with was less
  than 1.
Scientific notation expresses a
number in the form:
        M x   10n
                     n is an
 1  M  10          integer
  4 x 106    IF the exponents are
+ 3 x 10 6   the same, we simply
             add or subtract the
  7 x 106    numbers in front and
             bring the exponent
             down unchanged.
            The same holds true
  4 x106
- 3 x10 6   for subtraction in
            scientific notation.
  1 x 106
  4 x106    If the exponents are
+ 3 x 105   NOT the same, we
            must move a decimal
            to make them the
  4.00 x   10 4.00 x
              6      10 6

+ 3.00 x 10 5 + .30 x 106

              4.30 x 10 6
 Move the
 decimal on
 the smaller
A Problem for you…
      2.37 x   10 -6

    + 3.48 x 10 -4
 002.37 x 10 -6

  + 3.48 x 10 -4
    0.0237 x 10 -4

  + 3.48   x 10 -4

    3.5037 x 10 -4
            Scientific Notation
           Calculation Summary
               Adding and Subtracting
You must express the numbers as the same power
  of 10. This will often involve changing the decimal
  place of the coefficient.
              (2.0 x 106) + ( 3.0 x 107)
       (0.20 x 107) + (3.0 x 107) = 3.20 x 107

              (4.8 x 105) - ( 9.7 x 104)
       (4.8 x 105) - ( 0.97 x 105) = 3.83 x 105
            Scientific Notation
 Multiply the coefficients and add the exponents
                  (xa) (xb) = x a + b
        (2.0 x 106) ( 3.0 x 107) = 6.0 x 1013

                  (xa) / (xb) = x a - b
       (2.0 x 106) / ( 3.0 x 107) = 0.67 x 10-1
Divide the coefficients and subtract the exponents
      Nature of Measurement
Measurement - quantitative observation
                consisting of 2 parts

               Part 1 - number
             Part 2 - scale (unit)

                 20 grams
         6.63 x 10-34 Joule seconds
 Uncertainty in Measurement

A digit that must be estimated
is called uncertain. A
measurement always has some
degree of uncertainty.
          Precision and Accuracy
Accuracy – measure of how close a measurement
comes to the actual or true value of whatever is
being measured.
Precision – measure of how close a series of
measurements are to one another.

  Neither        Precise but not     Precise AND
accurate nor        accurate           accurate
    Why Is there Uncertainty?
 Measurements are performed with instruments
 No instrument can read to an infinite number of
decimal places
   Which of these balances has the greatest
   uncertainty in measurement?
              Determining Error

  Accepted Value – the correct
  value based on reliable references

  Experimental Value – the value
  measured in the lab

Error(can be +or-)=experimental value – accepted value

Percent error = absolute value of error x 100%
                   accepted value
          Significant Figures in
In a supermarket, you can use the scales to
   measure the weight of produce.

If you use a scale that is calibrated in 0.1 lb
   intervals, you can easily read the scale to the
   nearest tenth of a pound.

You can also estimate the weight to the nearest
  hundredth of a pound by noting the position of the
  pointer between calibration marks.
          Significant Figures in
If you estimate a weight that lies between 2.4 lbs
   and 2.5 lbs to be 2.46 lbs, the number in this
   estimated measurement has three digits.

The first two digits (2 and 4 ) are known with

The rightmost digit (6) has been estimated and
  involves some uncertainty.
          Significant Figures in
Significant figures in a measurement include all of
  the digits that are know, plus a last digit that is

Measurements must always be reported to the
 correct number of significant figures because
 calculated answers often depend on the number
 of significant figures in the values used in the
Rules for Counting Significant

Nonzero integers always count as
significant figures.

          3456 has
          4 sig figs.
Rules for Counting Significant

Leading zeros do not count as
  significant figures.

         0.0486 has
         3 sig figs.
Rules for Counting Significant

Zeros at the end of a number and
to the right of a decimal point are
always significant.
          9.000 has
          4 sig figs

          1.010 has
          4 sig figs
Rules for Counting Significant

  Captive zeros always count as
    significant figures.

           16.07 has
           4 sig figs.
Rules for Counting Significant
 Zeros at the rightmost end that
lie at the left of an understood
decimal point are not significant.
          7000 has
          1 sig fig

          27210 has
          4 sig figs
Rules for Counting Significant
Exact numbers have an infinite
number of significant figures.

1 inch = 2.54 cm, exactly
  Rules for Significant Figures in
     Mathematical Operations

Multiplication and Division: # sig figs in
the result equals the number in the least
precise measurement used in the

        6.38 x 2.0 =
    12.76  13 (2 sig figs)
Rules for Significant Figures in
   Mathematical Operations
Addition and Subtraction: The number
of decimal places in the result equals the
number of decimal places in the least
precise measurement.

       6.8 + 11.934 =
  18.734  18.7 (3 sig figs)
           Sig Fig Practice #1
How many significant figures in each of the following?

         1.0070 m        5 sig figs
           17.10 kg      4 sig figs

        100,890 L        5 sig figs

      3.29 x 103 s       3 sig figs
       0.0054 cm         2 sig figs
        3,200,000        2 sig figs
             Sig Fig Practice #2
   Calculation        Calculator says:     Answer
3.24 m x 7.0 m         22.68 m2            23 m2
100.0 g ÷ 23.7 cm3     4.219409283 g/cm3 4.22 g/cm3
0.02 cm x 2.371 cm 0.04742 cm2            0.05 cm2
710 m ÷ 3.0 s          236.6666667 m/s    240 m/s
1818.2 lb x 3.23 ft    5872.786 lb·ft     5870 lb·ft
1.030 g ÷ 2.87 mL      2.9561 g/mL       2.96 g/mL
             Sig Fig Practice #3
   Calculation        Calculator says:   Answer
3.24 m + 7.0 m           10.24 m         10.2 m
100.0 g - 23.73 g         76.27 g        76.3 g
0.02 cm + 2.371 cm        2.391 cm       2.39 cm
713.1 L - 3.872 L         709.228 L      709.2 L
1818.2 lb + 3.37 lb       1821.57 lb     1821.6 lb
2.030 mL - 1.870 mL       0.16 mL        0.160 mL
1) 78ºC, 76ºC, 75ºC 2) 77ºC, 78ºC, 78ºC
3) 80ºC, 81ºC, 82ºC
The sets of measurements were made of the boiling
  point of a liquid under similar conditions. Which
  set is the most precise?
Set 2 – the three measurements are closest together.
What would have to be known to determine which set
                is the most accurate?
The accepted value of the liquid’s boiling point
How do measurements relate to experimental

Making correct measurements is fundamental to the
  experimental sciences.
How are accuracy and precision evaluated?
Accuracy is the measured value compared to the
   correct values. Precision is comparing more than
   one measurement.
Why must a given measurement always be reported to the
   correct number of significant figures?

The significant figures in a calculated answer often depend on
   the number of significant figures of the measurements
   used in the calculation.

How does the precision of a calculated answer compare to the
   precision of the measurements used to obtain it?

A calculated answer cannot be more precise than the least
    precise measurement used in the calculation.
A technician experimentally determined the boiling
    point of octane to be 124.1ºC. The actual boiling
    point of octane is 125.7ºC. Calculate the error and
    the percent error.

Error = experimental value – accepted value
         error = 124.1ºC – 125.7ºC = -1.6ºC
Absolute error / accepted value x 100%
      % error = -1.6ºC / 125.7ºC x 100% = 1.3%
Determine the number of significant figures in each of
   the following
                  11 soccer player
                   0.070 020 meter
                    10,800 meters
                  5.00 cubic meters
Solve the following and express each answer in scientific
 notation and to the correct number of significant figures.

                (5.3 x 104) + (1.3 x 104)
                        6.6 x 104
                (7.2 x 10-4) / (1.8 x 103)
                        4.0 x 10-7
                    (104)(10-3) (106)
               (9.12 x 10-1) - (4.7 x 10-2)
                       8.65 x 10-1
                 (5.4 x 104) (3.5 x 109)
               18.9 x 1013 or 1.9 x 10 14
Don’t be scared!
  International Systems of Units
• The standards of measurement used in science
  are those of the metric system
• All metric units are based on multiples of 10
• Metric system was originally establish in France
  in 1795
• The International System of Units (SI) is a
  revised version of the metric system.
• The SI comes from the French name, le
  Systeme International d’Unites.
• The SI was adopted by international agreement
  in 1960.
  International Systems of Units
           There are seven SI base units
                     SI Base Units
    Quantity          SI base unit     Symbol
Length                   Meter             m
Mass                    kilogram           kg
Temperature              kelvin             K
Time                    second              s
Amount                   mole              mol
Luminous intensity      candela            cd
Electric current        ampere              A
               Metric Prefixes
Mega (M)
       Kilo (k) 103
             Hecto (hm) 102
                  Deka(da) 101
                       Meter (m)

left                       Deci (d) 10-1
                                 Centi (c) 10-2
                                      Milli (m) 10-3
right                                      Micro (µ) 10-6
                                             Nano (nm) 10-9
                                                Pico (pm) 10-12
          Metric Conversions
       1.0 decimeter (dm) = ? hectometers
             0.001 hectometer (hm)
2.5 hectometer (hm) = ? millimeters
250,000 millimeters (mm)
        9.7 centimeters (cm) = ? kiometers
            0.000097 kilometers (km)
7.4 grams (g) = ? Milligrams (mg)
7400 milligrams (mg)
Other Common Conversions
           1 cm3 = 1ml
           1dm3 = 1L
        1 inch = 2.54 cm
          1kg = 2.21 lb
           454 g = 1 lb
          4.18 J = 1 cal
    1 mol = 6.02 x 1023 pieces
          1 GA = 3.79 L
              Units of Length
meter – the basic SI unit of length or linear measure

Common metric units of length include the centimeter
 (cm), meter (m), and kilometer (km)
               Units of Volume
Volume -the space occupied by any sample of matter
Volume (cube or rectangle) = length x width x height
The SI unit of volume is the amount of space occupied
  by a cube that is 1m along each edge. (m3)
Liter (L) – non SI unit – the volume of a cube that is
 10cm along each edge (1000cm3)
The units milliliter and cubic centimeter are used
                        1 cm3 = 1ml
                       1dm3 = 1L
             Units of Mass
Common metric units of mass include the
 kilogram, gram, milligram and microgram.
Weight – is a force that measures the pull on a
 given mass by gravity.

Weight is a measure of force and is different than
Mass – measure of the quantity of matter.
Although, the weight of an object can change with
  its location, its mass remains constant
  regardless of its location.
Objects can become weightless, but not massless
         Units of Temperature
Temperature – measure of how hot or cold an
  object is.
The objects temperature determines the direction
  of heat transfer.
When two objects at different temperatures are in
 contact, heat moves from the object at the
 higher temperature to the object at the lower
Scientist use two equivalent units of temperature,
  the degree Celsius and the Kelvin.
          Units of Temperature
The Celsius scale of the metric system is named after
  Swedish astronomer Anders Celsius.
The Celsius scale sets the freezing point of water at
  0ºC and the boiling point of water at 100ºC
The Kelvin scale is named for Lord Kelvin, a Scottish
  physicist and mathematician.
On the Kelvin scale, the freezing point of water is
 273.15 kelvins (K), & the boiling point is 373.15 K.
With the Kelvin scale the degree (º) sign is not used
          Units of Temperature
A change of 1 º on the Celsius scale is equivalent to
  one kelvin on the Kelvin scale.

The zero point on the Kelvin scale, 0K, or absolute
  zero, is equal to -273.15º C.

                   K = ºC + 273

                    ºC = K - 273
               Units of Energy
Energy – the capacity to do work or to produce heat.
The joule and the calorie are common units of
The joule (J) is the SI unit of energy named after the
  English physicist James Prescott Joule.
1 calorie (cal) - is the quanity of heat that raises the
  temperature of 1 g of pure water by 1ºC.
                    1 J = 0.2390 cal

                     1 cal = 4.184 J
End of Section 3.2
            Conversion Factors
1 dollar = 4 quarters = 10 dimes = 20 nickels = 100 pennies

   Different ways to express the same amount of money

1 meter =10 decimeters =100 centimeters =1000 millimeters

            Different ways to express length
Whenever two measurements are equivalent, a ratio
 of the two measurements will equal 1.
                    1 m = 100 cm = 1
                                  Conversion factor
           Conversion Factors
Conversion factor – a ratio of equivalent
                     100 cm / 1 m
                   1000 mm / 1 m
The measurement on the top is equivalent to the
  measurement on the bottom
Read “one hundred centimeters per meter” and “1000
               millimeters per meter”
Smaller number        1m             larger unit
Larger number        100 cm         smaller unit
          Conversion Factors
When a measurement is multiplied by a conversion
 factor, the numerical value is generally changed,
 but the actual size of the quantity measured
 remains the same.
Conversion factors within a system of measurements
 are defined quantities or exact quantities.
Therefore, they have an unlimited number of
  significant figures and do not affect the rounding of
  a calculated answer.

How many significant figures does a conversion
 factor within a system of measurements have?
        Dimensional Analysis
Dimensional analysis – a way to analyze and solve
  problems using the units, or dimensions, of the
How many minutes are there in exactly one week?
60 minutes = 1 hour         24 hours = 1 day
                  7 days = 1 week

1 week 7 days 24 hours    60 minutes = 10,080 min
       1 week   1 day       1 hour

                 1.0080 x 104 min
        Dimensional Analysis
How many seconds are in exactly a 40-hr work

60 minutes = 1 hour        24 hours = 1 day
7 days = 1 week            60 seconds = 1 minute

40 hr 60 min 60 sec   = 144,000 s
       1 hr   1 min

                  1.44000 x 105 s
         Dimensional Analysis
An experiment requires that each student use an
  8.5 cm length of Mg ribbon. How many students
  can do the experiment if there is a 570 cm length of
  Mg ribbon available?

570 cm ribbon    1 student       = 67 students
                 8.5 cm ribbon

2 sig figs
         Dimensional Analysis
A 1.00º increase on the Celsius scale is equivalent to a
 1.80º increase on the Fahrenheit scale. If a temperature
 increases by 48.0ºC, what is the corresponding
 temperature increase on the Fahrenheit scale?

48.0ºC      1.80ºF = 86.4ºF

A chicken needs to be cooked 20 minutes for each
 pound it weights. How long should the chicken be
 cooked if it weighs 4.5 pounds?
               4.5 lb 20 min     = 90 min
         Dimensional Analysis
Gold has a density of 19.3 g/cm3. What is the density in

19.3 g 1 kg       1 x 106 cm3 = 1.93 x 104 kg / m3
 cm3 1000 g        m3

There are 7.0 x 106 red blood cell (RBC) in 1.0 mm3
 of blood. How many red blood cells are in 1.0 L of
7.0 x 106 RBC     1 x 106 mm3 1 dm3 = 7.0 x 1012
1.0 mm3              dm3        1L
        Dimensional Analysis
1.00 L of neon gas contains 2.69 x 1022 neon atoms. How
 many neon atoms are in 1.00mm3 of neon gas under the
 same conditions?

2.69 x 1022 atoms    1L      dm3
  1.00 L            1 dm3    1 x 106 mm3

         2.69 x 1016 atoms in 1.00mm3 of gas
What conversion factor would you use to convert between
 these pairs of units?

                   Minutes to hours
                 1 hour / 60 minutes

                 grams to milligrams
                    1000 mg / 1 g

            Cubic decimeters to milliliters
                   1000 ml / 1 dm3
An atom of gold has a mass of 3.271 x 10-22g. How many
 atoms of gold are in 5.00 g of gold?

              1.53 x 1022 atoms of gold
Light travels at a speed of 3.00 x 1010 cm/sec. What
 is the speed of light in km/hour?

                   1.08 x 109 km/hr
Convert the following. Express your answers in scientific

                    7.5 x 104 J to kJ
                       7.5 x 101 kJ

                   3.9 x 105 mg to dg
                       3.9 x 103dg

                  2.21 x 10-4 dL to µL
                      2.21 x 101µL
Make the following conversions. Express your answers in
 standard exponential form.

                     14.8 g to µg
                     1.48 x 107 µg

                  3.75 x 10-3 kg to g
                        3.72 g

                    66.3 L to cm3
                    6.63 x 104 cm3
If a piece of led and a feather of the same volume are
  weighted, the lead would have a greater mass than the
It would take a much larger volume of feather to equal
  the mass of a given volume of lead.
               Density = mass / volume
Mass is a extensive property (a property that depends on
 the size of the sample)

Density is an intensive property (depends on the
 composition of a substance, not on the size of the sample)
A helium filled balloon rapidly rises to the ceiling when

Whether a gas-filled balloon will sink or rise when
 released depends on how the density of the gas
 compares with the density of air.

Helium is less dense than air, so a helium filled
 balloon rises.
        Density and Temperature
The volume of most substances increase as the
 temperature increases.
The mass remains the same despite the temperature
 and volume changes.
So if the volume changes with temperature while the
 mass remains constant, then the density must also
 change with temperature.
The density of a substance generally decreases as its
 temperature increases. (water is the exception: ice floats
 because it is less dense than liquid water)
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 245cm3 and a mass of 612g.
 Was is the density? Is it aluminum?
           D = 612g / 245cm3 = 2.50g/cm3
D of aluminum is 2.70 g/cm3; no it is not aluminum
A bar of silver has a mass of 68.0 g and a volume of
 6.48 cm3. What is the density?

          D = 68.0g / 6.48 cm3 = 10.5 g/cm3
The density of boron is 2.34 g/cm3. Change 14.8 g of
 boron to cm3 of boron.
               D = m / v or v = m / D
            V = 14.8 g    cm3 = 6.32 cm 3
                         2.34 g

Convert 4.62 g of mercury to cm3 by using the density
 of mercury -13.5 g/cm3.

           V = 46.2 g     cm3 = 0.342 cm 3
                         13.5 g



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