Scientific Notation and Significant figures notes
-Scientific Notation Basics:



2 partsa. 1st Number must be between 1-10,
b. 2nd number is 10n Example. 2.0 x 103



Multiplication- add exponents
Division- subtract exponents
Addition and subtraction- both exponents need to be the same
To increase the exponent- move the decimal to the left.
--------- To decrease the exponent- move the decimal to the right.
-Significant Figures
1. When making measurements always approximate the last digit.
2. Leading zeros are never significant.
3. Imbedded zeros are always significant.
4. Trailing zeros are significant only if the decimal point is specified.
Hint: Change the number to scientific notation. It is easier to see.
5. Addition or Subtraction:The last digit retained is set by the first doubtful digit.
6. Multiplication or Division:The answer contains no more significant figures than the least
accurately known number.
Practice-Look up and study the website below. Make sure you can add, subtract, multiply, and divide using
scientific notation.
-Go to the bottom of the website and go to "Significant Figures". Go over the rules for using significant
figures with a partner. Together, complete the quiz. Write the questions and answers in the left side of
your notebook.
http://www.chem.tamu.edu/class/fyp/mathrev/mr-scnot.html
Unit Conversion
Dimensional Analysis: A method of converting units that displays each mathematical step and reduces
the probability of error.
Steps:
1. Estimate the magnitude of the final answer.
2. Write the measurement as a proportion.
3. Set up a multiplication problem.
4. Insert units so they will cancel.
5. Insert conversion factor(s).
6. Cancel units.
7. Multiply straight across.
Use the following website to practice - http://www.chem.tamu.edu/class/fyp/mathrev/mr-da.html
Measurement (Not needed in notes)
*All measurements are approximations.
Ex: *Meniscus: The curved surface created by surface tension when liquid is added to a container such
as a graduated cylinder.
Metric System (a.k.a. the International System of Units)
*Preventing conversions increases accuracy – measure in metric units to reduce conversions
*Convenient because it is based on a factor of 10
Measurement
Standard Unit
Length
= meter
Volume
= liter
Mass
= gram
Temperature
= Celsius degrees
Calculations Using Metric Units
Mass: The amount of matter an object contains
*Measured using a scale or balance.
Area: A calculation of how much surface an object has.
Area (A) = length (l) x width (w)
A= l x w
Volume: A calculation of the amount of space an object occupies.
Volume of a box (V) = height (h) x width (w) x length (l)
V=hxwxl
Volume of a cylinder (V) = π r2 x h
Density: The amount of matter an object contains per unit of volume.
Density (D) = mass (m) / volume (v)
D = m/v
Weight: The measure of the force of gravity on an object.
*Note mass is different from weight. Weight depends on the amount of gravitational force and is
measured in Newtons (N).
*Gravitational force equals 9.8 N on earth
Weight = mass in kg x gravitational force.
W = m(kg) x 9.8N
Ex: A 1 kg mass would weigh 9.8 N on earth.
Ex: If an object has a mass of 500 g, its weight would be:
W = m(kg) x 9.8N
= 0.5 kg x 9.8 N
= 4.9 N
Temperature Unit Conversion
Fahrenheit to Celsius Conversion for 98.6 oF :
°C = (oF – 32) x 5/9
Simplified Steps for 98.6 oF to °C
°F -32 = 66.6
66.6/9 = 7.4
7.4 x 5 = 37.0
Celsius to Fahrenheit Conversion for 37.0 °C:
o
F = (°C x 9/5) + 32
Simplified Steps for 37 °C to oF
°C x 9 = 333
333/5 = 66.6
66.6 + 32 = 98.6
Celsius to Kelvin Conversion for 37.0 °C:
Add 273 to convert to Kelvin or subtract 273 to convert to Celsius:
K = °C +273
K = 37.0 + 273
K = 310
°C = K - 273
°C = 310 -273
°C = 37
*Note the degree symbol is not used for Kelvin.