Factor Label Unit Conversion
Numbers alone, numbers without units, "naked numbers" are seldom used.
One of your blizzard bag questions is to find examples when it is okay to use a number without a unit.
The factor label unit conversion method is a way to convert an amount with one unit into an equivalent amount with a different unit. For example it shows how to convert from 200 cents to $2
If you do not have internet access, do the practice worksheet handed out in class and answer the questions below.
If you have internet access, go to the following website and do all the problems. Make paper copies of each problem you do. Also answer the questions below.
website: Factor Label Practice Problems
Read the article below "Naked Numbers Cost NASA" to understand why putting units with your numbers is important.
Questions for all to do:
1. Find times when it is okay to use a number without a unit.
2. Comment on how the following story can be possible:
I was driving north from Vermont to Quebec. After I entered Canada the speed limit changed from 65 to 100 so I slowed down a little.
3. Give an example when 1 = 1000
4. Find the unit that currently has the record for being the largest.
5. Why use units with your number?
Bring responses on paper to class tomorrow
Naked Numbers Cost NASA
Mars Climate Orbiter Gone Forever
After a nine month trip to Mars, the Mars Climate Observer spacecraft
was lost as a result of Naked Numbers. Numbers communicated from
Lockheed Martin in Colorado to NASA's Jet Propulsion Lab in California
were left unit-less. Naked numbers, being completely meaningless,
left engineers to guess at their meaning. The confusion created by
improperly dressed numbers caused the loss of a $125 million
spacecraft and the waste of a 9 month journey to Mars. Thankfully, no
lives were lost.
Lockheed Martin was sending daily course adjustments to the Jet
Propulsion Laboratory with numbers that should have been wearing the
English units of "pound-seconds" to describe the amount of impulse
which should be applied to the spacecraft to adjust its course. When
these naked numbers arrived at the Jet Propulsion Laboratory engineers
assumed that these were specifying the amount of impulse in metric
units of "newton-seconds". Simply labeling the units that were being
used would have prevented this tremendous loss. A group of physics
teachers in Ithaca, New York hope to bring a proposal to Capitol Hill
that would ban the use of naked numbers in the United States. Further
efforts are being used to convince the United Nations to apply a
similar law to the World. Until such a law is passed, physics
teachers everywhere will have to settle for simply marking answers as
wrong if they are not labeled with proper units. Math teachers are
urged to contribute to the solution not the problem.
Mars Orbiter Loss Linked to Math Mistake
Newsday - Ithaca Journal
October 1, 1999
Washington - The loss of the Mars Climate Orbiter as it approached
Mars last week is being blamed on a goof that could have tripped up a
novice science student - confusing English and metric units.
A preliminary investigation has found that two spacecraft teams -
one at NASA's Jet Propulsion Laboratory in Pasadena, Calif., and the
other at a Lockheed Martin facility in Colorado where the spacecraft
was built - unknowingly were exchanging some vital information in
different units of measurement.
Thomas Gavin, deputy director of space and earth sciences at JPL,
said in an interview Thursday that the mistake involved information
being used to make tiny corrections in the spacecraft's orientation
during its 9½-month cruise to Mars.
Twice a day during the cruise to Mars, tiny thrusters on the
spacecraft were fired briefly to counteract the effects of solar wind
and other forces on the spinning of the flywheels. The spacecraft
team in Colorado used English units called pound-seconds to describe
the small forces.(bad scienc writing)
That data was shipped via computer to JPL where the navigation
team was expecting to receive the information in newton-seconds, a
metric measure of force. (bad science writing)
Two Cornell University scientists calibrated the camera on the
spacecraft, but neither scientist had any involvement in the