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Scientific Measurement

Scientific Measurement: Presentation of Data

I. Scientific Notation


The speed of light = 300,000,000 meters per second
The mass of the earth = 6,000,000,000,000,000,000,000,000 kg
The mass of an electron = 0.000000000000000000000000000091 g
The wavelength of light = 0.000059 cm


A number written in scientific notation is in the form: ____________

where n = the _______________ and 1 < ______ < 10 
and m = the __________________ and m is a positive or negative integer

To express a number in standard scientific notation:

1) ______________________________________________________
________________________________________________________

2) ______________________________________________________
________________________________________________________

3) Write the _________________ as 10 raised to the power equal to the number from step 2.


4) If the decimal was moved to the _________, the exponent is _________; if the decimal was moved to the ________ the exponent is ____________ and a (-) sign is inserted before the exponent.

Example 1: Express 784,000 miles in scientific notation.

                            7    8    4    0    0    0.     miles





therefore, 105  ____________ because decimal was moved to the ________

Answer: ________________________ miles

Example 2: Express 0.00015 meters


                           0.     0      0     0    1     5  meters

 


therefore, ______    ________________ because decimal was moved to ______________

Answer: ___________________ meters

Example 3: Convert 428.5 x 10 9 seconds to standard scientific notation.

First convert 428.5 to scientific notation = ______________________ 

Now, you have 4.285 x 10 2 x 10 9

Answer:   ___________________________

Rules for exponents

1) (am) x (an) = a m+n

ex. 

2) a m = a (m-n)
    a n

ex. 
      

3) (a m) n = a mn


ex. 


4) n a m = a m/n


Calculations in Scientific Notation

1) When multiplying numbers in scientific notation, the coefficients are _______________ and the exponents are ______________.

(n x 10 m) (X x 10 y) = nX x 10 (m+y)

Example: Multiply 4 x 10 2 by 5 x 10 3

Solution: 

Answer = 


2) When dividing numbers in scientific notation, the coefficients are ________________, and the denominator exponent is _______________ from the numerator exponent.

n x  10 m x 10 (m-y)
X x 10 y     X

Example: Divide 7.5 x 10 6 by 2.5 x 10 2

Solution:
             


3) Adding or subtracting numbers in scientific notation, when both numbers are to the same power of 10, is done by adding or subtracting the coeffecients and keeping the same power of 10.

Example:  Add 5.0 x 105 kJ   and    4.8 x 105  kJ

Solution:

Answer:

Example: Add 2.52 x 10 4 and 2.43 x 10 3

Solution: 

Then:

Answer = 

Calculator Practice:


Example:         8.0 x 10 6   J
                       2.0 x 10 s

Solution (without calculator) = 8.0  x  10 (6-3) =  4.0 x 10 J/s
                                               2.0 

Solution (with calculator)

Enter 8.0, then press [2nd] [EE ] 6
You see 8.0 E 6

Now press [divided by]  2.0 [2nd] [ EE]  3
Press Enter
Answer: 4000 = 4.0 x 10 3   J/s

2) Example

45  meters 
(32 sec) (88 sec)

___________ Solution:
Enter 45
[Divide] by 32   x   88

Solution:

 








II. Significant Figures

A. Significant Figures

1. Meter Stick

Example 1:



Example 2:


Example 3:




Example 4:


2. Thermometer

Example 1:


Example 2:


3. Graduated Cylinder

Example 1:

Example 2:

4. Electronic Balance

 

 

 

 

 

 

 


B. Significant Figure RULES 

1. Digits other than zero are always significant.

Example:    45.85 g has _________ significant figures


2. Zeros between other digits, whether to the left or the right of the decimal point are significant.

Example. 405.85 g has _____ significant figures

Example. 45.805 g has ______ significant figures


3. Zeros to the right of the decimal point are significant when positioned to the right of the last nonzero digit. 

Example. 16.100 g has _____ significant figures

Example. 2.500 x 103 m has ______ significant figures

Example. 2500 m has ______ significant figures



4. Zeros to the left of the first nonzero digit are not significant.

Example. 0.00078 kg has _____ significant figures



5. Zeros to the left of the decimal point on numbers less than one are 
not significant.

Example:

6.  Exact numbers have an infinite number of significant figures.

Example:

Example:


C. Math with Significant Figures

1. Addition and Subtraction with Significant Figures

a) Count the number of significant figures in the decimal portion of each number in the problem.

b) Add or subtract as indicated in the problem.

c) Round the answer so that is contains only as many decimal places as the number in the problem that contains the LEAST number of decimal places.

Example:                 345.98 g + 78.8 g

Solution: 

                   Number of sig figs after decimal pt: 


Answer = __________ g


Example:                      677.1 cm - 20.98 cm

Solution:
677.1 cm - 20.98 cm = ____________
Number of sig figs after decimal pt: _______

Answer = ___________ cm


2. Multiplication and Division with Significant Figures

The LEAST number of significant figures in any number of the problem determines the number significant figures in the answer.


Example 1: 

(1.13 m) x (5.1267 m)

Solution:                (1.13 m) x (5.1267 m)    =    _______ m 2
Number of sig figs:     _____        _____ 
 
Answer = _________ m 2


Example 2: 

6789.7 m / 60.0 s

Solution: 

6789.7 m / 60.0 s = _______ m/s
number of sig figs: ______ / ______ 


Answer = _________ m/s


Example 3: 

2.897 x 102 m 2 / 3.4 x 10 m

2.897 x 102 m 2 / 3.4 x 10 m = _______ m
number of sig figs: _____/ _____

Answer = __________ m


REVIEW OF SIG FIGS


III. Units

A. Seven Base Units


Physical Quantity                 Name of SI unit                      Symbol for SI unit

length                                     meter                                         m

mass                                      kilogram                                    kg

time                                       second                                       s

electric current                       ampere                                      A

temperature                           Kelvin                                       K

amount of substance               mole                                         mol

luminous intensity                   candela                                     cd

1 meter is the distance light travels in a vacuum in 1/299,792,458 second.

1 kg is a platinum-iridium cylinder.

1 second is 9,192,631,770 oscillations of cesium atoms absorbing microwave radiation.



Non SI units used often in Chemistry:

1) Liter = L                                                                measure of volume

2) Cubic centimeters = cm3                                                     measure of volume   (1 mL = 1 cm3)

3) Angstrom = A                                                       measure of length      (1 A = 10-8 cm)


B. Metric Prefixes

Prefix     Symbol      Numerical Multiplier                                  Exponential Factor
yotta        Y          1,000,000,000,000,000,000,000,000             10 24
zetta         Z          1,000,000,000,000,000,000,000                    10 21
exa           E          1,000,000,000,000,000,000                           10 18
peta          P          1,000,000,000,000,000                                  10 15
tera           T          1,000,000,000,000                                         10 12
giga          G          1,000,000,000                                                 10 9 *
mega        M         1,000,000                                                        10 6 *
kilo           k          1,000                                                               10 3 *
hecto        h           100                                                                  10
deca        da          10                                                                    10 1
no prefix means:     1                                                                      10 0 *
deci         d            0.1                                                                   10 -1 *
centi        c             0.01                                                                 10 -2 *
milli         m            0.001                                                               10 -3 *
micro                     0.000001                                                         10 -6 *
nano        n             0.000000001                                                    10 -9 *
pico         p             0.000000000001                                              10 -12 *
femto       f              0.000000000000001                                        10 -15 *
atto         a              0.000000000000000001                                  10 -18  
zepto       z              0.000000000000000000001                            10 -21  


C. Units Derived From Base Units

1. Area
length x length 

units:    m 2, cm 2, etc.

2. Volume  (the amount of space an object takes up)

length  x  length  x  length
units:   m 3,  cm 3,  or mL,  L,  etc.   (SI unit is ______)
Vrectangular solid = L x W x H
Vcylinder = D 2 H
                     4 


3. Pressure (force exerted per unit of surface area)

units:     N/m 2,   Pa (pascal),  atm,  mm Hg,  etc.

Note:  Extensive vs. Intensive Properties

_______________________________ - depends on the amount of substance present

_______________________________ - independent of the amount of substance

4. Energy  (the capacity to do work)

(kg x m 2 ) / s 2

 units: J (joule),  calorie

5. Density

symbol = 

____________________ property

definition:

 

equation:

 

Examples:

1)  A block of aluminum occupies a volume of 15.0 mL and has a mass of 40.5 g.  What is the density?

 

 

2)  Mercury metal is poured into a graduated cylinder that holds exactly 22.5 mL.  The mercury used to fill the cylinder has a mass of 306.0 g.  From this information, calculate the density of mercury.

 

 

3)  Find the mass of 250.0 mL of benzene.  The density of benzene is 0.8765 g/mL.

 

 

4)  What volume of silver metal has a mass of exactly 2500.0 g?  The density of silver is 10.5 g/cm3.

 

 

 

Challenge Density Problems:

1)  Lithium is a soft, gray solid that has the lowest density of any metal.  It is an essential component of some advanced batteries.  If a small rectangular slab of lithium weighs 1.49 x 103 mg and has sides that measure 20.9 mm by 11.1 mm by 11.9 mm, what is the density of lithium?

 

 

 

 

2)  Galena, an ore of lead, has a volume of 4.6 cm3.  If the density of galena is 7.5 g/cm3, what is the mass (in kg) of that piece of galena?

6.  Measuring Temperature

Temperature 

          - a measure of how hot or cold a substance is relative to another substance

          - determines whether there can be heat transfer from one object to another and determines the direction of heat flow

          - temperature is an ________________________property

Three temperature scales in use today:

 

 

Temperature Conversions:

 

 

 

 

 

 

 

Sample Problems::

1) Your normal body temperature is 98.6oF.  Convert this temperature to oC.

 

 

2)  Many laboratories use 25 oC as a standard temperature.  What is this temperature in oF? in K?

 

 

3)  Liquefied nitrogen boils at 77 K.  What is this temperature in oC?

 

 

7.  Measuring Time

 

 

 

8.  Qualitative and Quantitative Measurements; Precision and Accuracy

 

 

 

 

___________________________________  -  descriptive, nonnumerical form

___________________________________  -  results in a number and unit

 

_____________________________ - how close a measurement is to the real value

_____________________________ - how close the measurements in a series are to each other

 

To evaluate accuracy:  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

HOMEPAGE