Measurement- Chapter 2

 

***A  measurement is  ________________________ data, consisting of a ____________ and a unit.

 

15     liters

Measurements must be:

v     Accurate:

 

 

v     Precise:

 

 

 

 

 

 

 

 

 

 

How to Calculate Percent Error

Percent Error

(definition)

 

 

Equation

 

 

 

 

 

Example:

A student measured an unknown metal to be 1.50 grams.  The accepted value is 1.87 grams.  What is the percent error? 

 

 

 

 

 

 

You try! 

Normal Boiling point is 100 °C.  A student measured the boiling boint of his sample to be 99.1° C.  What is the percent error?

 

 

 

 

 

 

                                                                                    UNITS

ENGLISH

METRIC

 

 

 

Ex.

 

 

 

 

Ex.

 

What are the base units of importance?

1.

 

2.

 

3.

 

4.

 

5.

 

6.

 

7.

 

What are some derived units?

1.

 

2.

 

 

Metric Prefixes: used to describe smaller or larger amounts of the base units                                            

 

KING                    HENRY                   DIED                      BY                     DRINKING       CHOCOLATE           MILK

 

Kilo

Hecto

Deka

base

deci

centi

milli

k

 

 

 

 

 

 

1000

 

 

 

 

 

Other Prefixes to use:

 

 

Converting Between Metric Units: Quickie Method: 

Within the metric system:  Use the chart above and determine how many spaces separate the 2 prefixes.  Then move the ____________________ in the value the number of places in that same direction.

           Examples                                                                                    You Try

          

Convert 22340 m into Km                                                  Convert 16386.2 ml into liters

 

 

 

Convert .3876 Hg into grams                                             Convert  100 J into cJ

 

 

Converting Between Metric Units and/or Between Metric and English units:

DIMENSIONAL ANAYSIS

 

v     A problem solving approach where _______________ cancel each other out.

 

v     You must use a _________________________ which is a fraction or __________ where 2 different units are equal to each other.

 

Examples:

 

 

 

 

To Convert using Dimensional Analysis:                                Convert 1500 m to km

1.  Place the quantity known.

 

1500 m

 

2.  Draw an elongated cross.

 

 

1500 m____________

 

3. Insert the unit from the known quantity on the

    ________________ of the fraction.

 

1500 m____________

                           m

 

4.  Insert the “wanted” unit in the ____________

 

1500 m ___ ____km____

                              m

 

 

5.  Insert numbers that equate the 2 units in the

     ratio. Cancel out units that are the same on

      top and bottom.

 

1500 m__ ___       1__km____

                         1000    m

 

 

6.  Multiply the numbers on top. Multiply the

     numbers on bottom and divide the bottom into

      the top.

 

1500 x 1   =   1500    =  1.5 km

   1000           1000

 

You Try:

Convert 85 quarters to dollars.                                 Convert 15 cm to m.

 

 

 

 

 

Convert 1 day into seconds

 

 

 

 

______________________________________________________________________________

Refer to “Measuring & Converting Length Measurements” Activity

 

Making Measurements and Significant Figures

v     Significant figures are __________ numbers within a measurement known to be true plus an ______________________ number.

 

v     You can only be as ___________ as the instrument you are using. (Look at the smallest marks)

 

 

v     The _____________ marks , the more ____________, the better the estimate.

 

v     Only measurements have significant figures.

 

v     _________________ numbers are exact.  1 dozen = 12 units;  2.54 cm = 1 inch

 

Rules For Counting Sig Figs

  1. All nonzero numbers are signifigant and are counted.

 

  1. _______________ are questionable.  See the short cut rule below:

 

SHORT CUT RULE:   DOT Right, NOT Left

If you see a decimal point, go to the _________________ end of the number and move right until the first non zero number.  Count it and ____________ number after it.

 

.123                _______ sig figs                                           4.5600           ______ sig figs

 

 

 

 

If you do not see a decimal point, go to the ________________ end of the number and move _____________  until the first nonzero number.  Count it and every number after it.

 

40506             __________ sig figs                                                65000           ______ sig figs

 

 

 

You Try!

987                             2076                           .078                            .09105                        5.670 x 104               

 

 

 

PROBLEM:  50 has only 1 sig fig.  How can we make it 2 sig figs?

 

 

 

Rounding     Rules

v     Look at the number _____________ the one you are rounding.  If it is _______________, don’t change it.  If it is ______________, make it bigger by one.

 

Examples:

314.721  (4)                                                               .0001775  (2)

 

 

8792   (2)                                                                   64.32 x 10-1  (1)

 

 

Sig Fig Math

Addign and Subtracting

Your answer will be rounded to the least precise measurement, the one with the least number of places to the right of the decimal point

  27.93

+  6.4 

  34.33       à   ___________

Multiplying anf Dividing

Your answer will be rounded to the least number of sig figs within the probelm

3.6 x 653 = 2350.8 

                          à ______________

 

You Try!

12.52 + 349.0 + 8.24 = _________________

 

74.626 + 28.34 = ________________

 

61.2    - 9.35 = ________________

 

7.55 x .34 = _____________

 

2.4526/8.4 = _______________

 

******Multiple Operations:  When problem contains all mult/div, don’t round till the end!

                                              If a mixture of add/sub and mult/div, do the rules for

                                              the  add/subtract, then the rules for the mult/div.

Refer to Significant Figure Dry Lab

 

Scientific Notation

M x 10n                     m = number between 1 and 10               n = whole number (exponent)

 

To go from Ordinary notation to Standard scientific notation

  1. Move the decimal point to a number between ________________
  2. The number of places you moved equals the exponent.
  3. If you move __________________, the exponent is positive.

 

Ordinary notation               65000                         Standard scientific notation             6.5 x 104

 

 

  1. Move the decimal point to a number between 1 and 10
  2. The number of places you moved equals the _____________.
  3. If you move right, the exponent is ______________.

 

Ordinary Notation               .0012                Standard scientific notation              1.2 x 10-3 

 

 

To go from  Standard scientific notation to Ordinary notation

v     Reverse the process from above.

v     Move the decimal point the number of places the ________________ tells you.  If it is positive, move right; if it is negative, move left.

 

6.730 x 10 -4                          _________________

           

5 x 10 x 10 2                                   _________________

 

3.010 x 10-6                           _________________

 

Measurements You Will Make In Lab:

 

Type                                         Definition                   Instrument Used             Metric Unit

 

Length

 

 

 

 

 

 

 

 

v     Mass

 

 

 

 

 

 

 

 

Ø      Volume

 

 

 

 

 

 

 

 

ü      Temperature

 

 

 

 

 

 

 

 

 

v     Mass and Weight are different from each other.  __________________ is the amount of matter as the force of gravity is pulling down on it.  It changes with __________________.  Mass stays ______________.

 

Ø      When reading volume, you must look at the bottom of the curved line called a _________________________.

 

ü      _____________________ is -273 °C.   or 0 ______________.

 

 

What are the 3 temperature scales?

 

 

 

 

 


Conversions between the Scales

                Between  ° C and ° F

          Between ° C and K

 

 

 

 

 

 

 

Examples

A child has a temperature of 38.7 °C.  Does she have a fever if normal body temperature is 98.6°F?

 

 

 

 

Mercury melts at 234 K.  What is its melting point  in Celsius and Fahrenheit?

 

 

 

Density

Definition:

 


Equation:                 

 

 

 

 

v     Is ice more or less dense than water?  Does it float or sink?

 

v     You can measure the _________________ of an object by water displacement.  The volume is the difference between the _________________ and initial volume of the water.

 

 

 

v     Density varies  with _____________________.

                               

                                                                            Why?                            

 

 

 

 

Density Problems:

Is it Aluminum?  The metal has a mass of 612 grams and a volume of 345 cm3.

What is the volume of a piece of wood that has a mass of 95.1 g and a density of .857 g/cm3?

Diamond has a density of 3.26 g/ml.  What is the mass if the volume is .35 ml?

 

 

 

 

 

 

 

 

 

 

 

 

 

Graphs

The general form of a straight line is:             y = mx + b

 

What does “m” represent?

 

What does “b” represent?

 

Sketch a graph representing:

A directly proportional relationship                                   Am inversely proportional relationship

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Refer to the Density Graphical Analysis Lab

 

Practice Links:

Accuracy & Precision:  http://lrc-srvr.mps.ohio-state.edu/shell-cgi/world/genquiz.pl

Counting Sig Figs: http://science.widener.edu/svb/tutorial/sigfigures.html

Adding /Subtracting Sig Figs: http://lrc-srvr.mps.ohio-state.edu/shell-cgi/world/genquiz.pl