Analyzing Data: Units &
Measurements
Units
• Le System Internationale d'Unites (SI measurement) is an internationally
agreed upon system of measurements
•
Prior systems would vary, even if they used the same/similar naming
• A base unit is a defined unit of measurement that is based upon some
object or event in the physical world and is independent of all other units of
measurement
• A prefix is added to specify for larger or smaller measurements
Units
• Time – Second (s)
•
Based on the frequency of radiation given by a cesium-133 atom
• Length – Meter (m)
•
The distance light travels in a vacuum in 1/299792458th of a second
• Mass – kilogram (kg) or gram (g)
•
1 kilogram is approximately 2.2 pounds (based on Earth's gravity)
• Temperature – Kelvin (K)
•
•
Absolute Zero (0K) is the point at which kinetic energy does not exist
Other systems include Celsius (used by scientists in labs) and Fahrenheit
Derived Units
• Not all quantities or measurements can
be measured with the SI base units –
some require a combination or 2 or more
bases units
• Volume – cubic meter (m3) or liter (L)
•
1L = 1 dm3 (1000 cm3 = 10cm x 10cm x 10cm)
• Density – the amount of mass per unit of
volume (g/cm3)
•
Density = mass/volume
Analyzing Data: Scientific
Notation & Dimensional
Analysis
Scientific Notation
• A system in which extremely large or small numbers are expressed as a
number between 1 and 10 (coefficient) multiplied by 10 raised to some
power (the exponent)
•
•
The exponent is determined by the direction and number of places a decimal is moved
A move to the left gives a positive exponent; a move to the right gives a negative
exponent
Magic Ruler
Kilok*
Hectoh*
Decada*
Base Unit
*
Decid*
Centic*
Millim*
1000
100
10
1
0.1
0.01
0.001
x 103
x 102
x 101
x 100
x 10-1
x 10-2
x 10-3
Calculations with Scientific Notation
• Addition and Subtraction
•
•
•
The exponents must be the same – rewrite values if needed
Add or subtract the coefficients (normal calculation)
Rewrite the answer & exponents if not in scientific notation
Calculations with Scientific Notation
• Multiplication and Division
•
Multiplication
•
•
Multiply the coefficients; add the exponents
Division
•
Divide the coefficients; subtract the exponents (divisor from dividend)
Dimensional Analysis
• A systematic approach to problem solving – allows us to convert units of
measurement while still measuring the same object
•
•
Equivalence Statement – showing equal measurements with different units of
measurement
Conversion Factor – a ratio made from an equivalence statement – for each problem,
MUST be written so that one unit is cancelled and a new unit is introduced