Physics 122 and 111

Review of the Math Toolbox

 

Scientific Notation

 

            Scientists work with large and small numbers. These numbers take up to much space and are hard to put into calculators. We use shorthand where we express decimal places as power of 10.

 

                        M x 10n          where 10> M >/= 1

                                             and n is an integer

 

            Move the decimal until only 1 non-zero digit remains on the left. Next count how many places the decimal has been moved and use the number as the exponent of 10.

            Remember      

                                     – the exponent becomes larger as the decimal moves  to the left

-   the exponent becomes smaller as the decimal moves to the right

 

Significant Digits (figures)

 

            Uncertainty in measurements: Due to two things

external causes – the device used may be inaccurate (metal rulers expands with temperature or electronic devices are affected by magnets)

 

            human error – this is caused by parallax (the apparent shift in the position of an object when it is viewed from various angles)

 

Precision – the degree of exactness to which the measurement of a quantity can be reproduced

 

ACCURACY – is the extent to which a measured value agrees with the standard value of a quantity

 

SIGNIFICANT DIGITS – all the digits that are certain plus a digit that estimates the fraction of the smallest division of the measured scale.

 

There are 4 rules for identifying significant digits:

1.                                                                   all non-zero digits are always significant

2.                                                                   all zeros between two non=zero digits are significant

3.                                                                   zeros after the decimal and last in the number are significant

4.                                                                   zeros after the decimal and first in the number are not significant (place holders)

 

 

 

 

 

 

 

 

The result of any mathematical operation with measurements can never be more precise that the least precise measurements (2 rules)

 

1.                                                                   When adding and subtracting you can find the least precise measurement by counting the places after the decimal. The measurement that has the smallest number of digits after the decimal is least precise and your answer can have no more places that this one.

 

2.                                                                   When multiplying and dividing you can determine the least precise measurement by counting the significant digits it has. The least precise measurement is the one with the least sig. figs. Your answer can have no more sig. figs. Than this measurement.

 

Manipulating Formulas

 

Relationships between variables are represented by equations. When rearranging formulas you must remember that when you do something to one side of the equation you must do the exact thing to the other side.

 

                        Y = mx + b       rearrange for b

                        y-mx = mx + b –mx

                        y – mx = b

 

The Metric System

 

            Created by a French scientist in 1795

            Convenient to use because its units are related by powers of 10

            International system if units (SI)

 

            Fundamental units                                                                    Derived units

-                                                                                  meter (m)  SI unit of length                                         -A combination of

-                                                                                  second (s) – SI unit of time                                        the fundamental          

-                                                                                  kilogram (kg) – SI unit for mass                                  units (m/s. kg/L)

 

 

metric prefixes

 

tera      giga     mega    kilo    hector    deka     meter     deci     centi    milli   micro    nano    pico

  T          G          M        k          h           da       root          d         c         m       u            n         p

1012     109        106       103      102        101       100        10-1      10-2     10-3    10-6      10-9    10-12

 

            Large measurements                                                     small measurements