Math & Measurement Reference Sheet for Physics
I.
II.
Scientific Notation: This is a shorthand mathematical “language” that you must be able to
read and write in order to function in physics.
a. Some websites that will help you master scientific notation are:
i. http://www2.ucdsb.on.ca/tiss/stretton/Basic_skills/Exponent.html
ii. http://www.nyu.edu/pages/mathmol/textbook/scinot.html
iii. http://janus.astro.umd.edu/astro/scinote/
b. It is VERY IMPORTANT that you type these numbers into your calculator correctly.
Typing 4 x 10 ˆ3 is INCORRECT, even if it sometimes seems to work. You must type
numbers into your calculators using the following steps, or your results will often be
wrong:
i. Punch the coefficient into your calculator.
ii. Push the EE or the EXP button (depending on your calculator.)
iii. Enter the exponent number and use the +/- button to change its sign if
necessary.
c. Calculating with scientific notation:
i. Multiplication & Division: The input (factor, dividend, and/or divisor) with the
fewest digits determines how many digits should be in your answer. Then use
rounding rules.
4.1 X 2 = 8
(3.0 E 8) x (2.00 E 2) = 6.0 E 10
ii. Addition & Subtraction: The input (term) with the fewest digits after a decimal
determines how many digits after the decimal there will be in the answer. If
none of the inputs have digits after a decimal, then keep all digits when adding
and subtracting. Then use rounding rules.
4.2 + 3.22 = 7.4
1,900,201 + 302 = 1,900,503
SI Units
a. You must use SI units in all of your calculations in physics class. I expect that you
understand what SI units are and why we use them. To help you, please reference:
i. http://www2.ucdsb.on.ca/tiss/stretton/Basic_skills/Metric_Skills.htm
ii. http://www2.ucdsb.on.ca/tiss/stretton/Database/Metric.html
b. The base units and prefixes are listed on your formula sheet. Note that the only
measurement whose “base unit” has a prefix is mass, which must be in kg before
performing calculations.
c. I expect that you are able to perform unit conversions (e.g., 4 E 3 mm = 4 E -3km.) If you
need help with this, please go to
http://www2.ucdsb.on.ca/tiss/stretton/Basic_skills/Dimensional_Analysis.html.
III.
IV.
Accuracy, Precision, and Uncertainty
a. I expect that you can distinguish between accuracy and precision.
i. Accuracy: How close to the true value is the measurement?
ii. Precision: The precision of a measuring instrument is determined by the
smallest unit to which it can measure. The precision is said to be the same as
the smallest fractional or decimal division on the scale of the measuring
instrument. A typical meterstick is precise to 1mm (or 0.001m.)
b. Uncertainty: In physics, unlike in chemistry, we use uncertainty instead of significant
figures.
i. When making measurements: Do NOT make estimated digits. Instead, measure
to the smallest unit on the measuring device and determine which of these
smallest units is closest to the true value.
ii. Then report the uncertainty. To determine the uncertainty of a measurement,
add and subtract (“+/-“) one-half of the precision of the measuring
instrument. Example:
INCORRECT: 41.63cm (3 is an estimated digit. The black object
is between 41.6cm and 41.7cm, and I estimated that it was 0.3 mm between the two.)
CORRECT: This is 0.416m +/- 0.0005m (or 416mm +/- 0.5mm or 41.6cm +/- 0.05cm
if measuring in mm or cm.)
Graphing: I expect that you can create and read graphs.
Dependent Variable vs. Independent Variable
Title
Put a circle around each point
you plot before interpolating
(connecting the points.)
Dependent
variable (unit)
The effect variable
Independent variable (unit)
The cause variable