Determining a Unit Conversion Factor
Yes, conversion factors can be looked up very quickly but how conversion factor is determined? Here the student will
determine several conversion factors for measurements of Length or Distance, Area, Volume and Temperature (This is a
tricky one. )
THIS IS INDIVIDUAL WORK, YOU MUST MAKE ALL YOUR OWN MEASUREMENTS. IF YOU HAVE THE SAME VALUES AS
ANOTHER STUDENT YOU WILL NOT RECEIVE CREDIT FOR THIS ASSIGNMENT.
Record your data and complete your work on the Data Sheet provided in class.
PART 1 – Measurements of LENGTH
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Use a ruler with English Units (Inches) and Metric Units (Centimeters) and measure 10 different items with both scales.
(Items can be anything, including just measuring lines you draw on paper)
Record your data.
Create two (2) graphs of your data
o Inches (Y-Axis) vs Centimeters (X-Axis)
o Centimeters (Y-Axis) vs Inches (X-Axis)
Use a ruler to Draw a Line of Best fit.
Select and mark 2 points on the Line of Best Fit and mark them on each graph.
Estimate the x and y values of the marks created on the Line of Best Fit.
Use the marks you selected to calculate the Slope of the Line.
Answer the Questions provided.
PART 2 – Measurements of AREA
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Use a ruler and do your best to draw a square 1” on a side.
Inside the square you have just drawn, use the metric ruler to see how many square centimeters you can draw.
Count the number of square centimeters that fit in the 1” square. ** It will be an estimate because it is not a whole
number. Do your best**
Record the Data
Repeat the above process for a square with sides of 2”. This should create 4 square inches right?
Create two (2) graphs of your data
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o In (Y-Axis) vs cm (X-Axis)
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o cm (Y-Axis) vs In (X-Axis)
Graph the data (Y-Axis) vs (X-Axis)
Use a ruler to Draw a Line of Best fit.
Select and mark 2 points on the Line of Best Fit and mark them on your graph.
Estimate the x and y values of the marks created on the Line of Best Fit.
Use the marks you Selected to calculate the Slope of the Line.
Answer the Questions provided.
PART 3 – Measurements of Volume
You should now understand the process well enough to apply it to volume. Use the kitchen measuring cups and water to
determine the conversion factors between cups and milliliters.
PART 4 – Measurements of Temperature
Conversions between temperature scales are much different that most unit conversions. Most unit conversions use a single factor to
either divide or multiply. Their equations are simple Linear Equations with a Y-Intercept of Zero, Y = mX. Temperature conversions
are through a standard Linear Equation, Y = mX + b. This is simply because the people that create the temperature scales we use
today did not make the best decisions in assigning the value of zero. Read the description below of how the temperature scales were
created.
The Celsius (also known as centigrade) temperature scale is the overwhelmingly popular scale around the world.
Americans are really the only folks stubborn enough to hang on to our old habits.
Anders Celsius, (1701 – 1744) born in Uppsala Sweden, was one of a large number of scientists (all related)
originating from Ovanåker in the province of Hälsingland. The family name is a Latinized version of the name of the
vicarage (Högen). His grandfathers were both professors in Uppsala: Magnus Celsius the mathematician and Anders
Spole the astronomer. His father, Nils Celsius, was also professor in astronomy. Celsius, who was said to have been
very talented in mathematics from an early age, was appointed professor of astronomy in 1730. For his
meteorological observations he constructed his world famous Celsius thermometer, with 0 for the boiling point of water and 100
for the freezing point. After his death in 1744 the scale was reversed to its present form.
http://www.astro.uu.se/history/Celsius_eng.html
What can be considered the first modern thermometer, the mercury thermometer with a standardized scale, was
invented by Daniel Gabriel Fahrenheit (1686-1736) in 1714.
The Fahrenheit scale divided the freezing and boiling points of water into 180 degrees. 32°F was the freezing point
of water and 212°F was the boiling point of water. 0°F was based on the temperature of an equal mixture of water,
ice, and salt. Daniel Fahrenheit based his temperature scale on the temperature of the human body. Originally, the
human body temperature was set 100° F on the Fahrenheit scale, but it has since been adjusted to 98.6°F.
Use the information from the reading above to determine the conversion from Celsius to Fahrenheit.
PART 5 – CREATE YOUR OWN TEMPERATURE SCALE – Tricky!!!
(Now you may work as a group but all
students must submit their own work) Groups no larger than 3 students.
This is a tricky exercise requiring a good deal of creativity. You need to think on your own a lot. Sorry but it’s time to be
independent thinkers.
Materials: You are welcome to use common measuring tools, a hot plate if necessary, water, ice (none are required)
Goal: Create a temperature scale of your own.
It can not be based on the C or F scale.
Products: You will be given a blank thermometer, you create a scale on paper to attach to the blank thermometer.
 You determine the spaces between the lines
 You determine the numbers on the lines
 You name the scale
 You determine the conversion between your scale and the C scale
Strategies: There are many strategies that you may take, if you can not think of your own feel free to follow one
described below:
 Strategy 1 - Measure the thermometer with a ruler and divide it evenly into whatever number of divisions you
would like (YOU CHOOSE) then make the scale and determine the # to place on it.
 Strategy 2 – Determine two temperatures common in life ( room temp, tap water temp, ice temp, person’s
temp, hot tap water temp, etc), find out where they end up on the blank thermometer, mark them. Then divide
the distance in to whatever # of degrees you would like.
 Strategy 3 – Think of your own strategy.