A unit is part of the quantity, not a label attached afterwards. It travels through every calculation.
Step 1: Something to Notice
Watch first. The explanation comes later.
The Mars Climate Orbiter was lost in 1999 because one team supplied thrust in pound-seconds and another expected newton-seconds. The arithmetic was correct throughout.
How does a correct calculation destroy a spacecraft?
Step 2: Find Out
Isolate the setup: arrange a conversion so the unwanted unit cancels, and confirm the remaining unit is the one you wanted.
Step 1 — Predict
A conversion is set up the wrong way round. What tells you before you calculate?
Choose what you think will happen. You cannot see the experiment until you do — guessing first is what makes it worth watching.
Step 3: So Here Is Why
Now the explanation, after you have seen it happen.
A conversion factor equals one
100 cm over 1 m is one, because they are the same length. Multiplying by one changes units, not quantity.
Conversion factor A fraction equal to one, written with different units above and below.
Arrange it so the unwanted unit cancels
Put the unit you want to remove on the bottom. The arithmetic then follows without a rule to remember.
The remaining unit is the check
A wrong setup leaves a unit that is not what you wanted, and it is visible before the arithmetic runs.
Chain as many as you need
Several factors in a row work the same way, each canceling the unit the last one produced.
Let the units tell you if you are right
Write each conversion as a fraction and cancel units until only the wanted one remains. If the units do not cancel to the right answer, the setup is wrong regardless of the arithmetic.
Chains of any length work the same
Grams to moles to particles is three factors in a row. The method does not become harder with more steps, which is why it is the standard approach to every conversion in the course.
Step 4: A Common Mistake
Lots of people think
“You have to remember whether to multiply or divide for each conversion.”
Step 5: Why SI Prefixes Are Powers of Ten
The same idea somewhere new.
Kilo, centi and milli are 10³, 10⁻² and 10⁻³, so every conversion within SI is a shift of the decimal point rather than a remembered factor. That is a design decision — the imperial system needs 12, 3, 1760 and 16 for lengths and weights, which is why unit errors are far more common when it is involved.
Step 6: Think It Through
Practice makes it stick.
The Wrong Way Round
Problem 1 of 2
A student computes 2.5 m × (1 m / 100 cm). What unit does the answer carry?
The Orbiter
Problem 2 of 2
Every calculation on the Mars Climate Orbiter was arithmetically correct. What went wrong?
Tracking the Units
1 of 5
Why does a conversion factor not change the quantity?
2 of 5
Where do you put the unit you want to remove?
3 of 5
When does the unit check catch an error?
4 of 5
Why are SI prefixes powers of ten?
5 of 5
Can several conversions be chained?
Step 7: Quick Check
Show what you know.
Question 1 of 1
Do you need to remember whether to multiply or divide for a conversion?
Step 8: Explain It in Writing
Claim, evidence, then reasoning.
The question
Explain how tracking units through a calculation catches an error, using the Mars Climate Orbiter as your case.
Fill in all three boxes. The reasoning box is the one that matters most.
What You Found Out
- A unit is part of the quantity and travels through the calculation.
- A conversion factor equals one, so it changes units without changing the quantity.
- Put the unwanted unit on the bottom so it cancels.
- The remaining unit checks the setup before any arithmetic runs.