A measurement is a number and a unit. Either alone is meaningless.
Step 1: Something to Notice
Watch first. The explanation comes later.
The Mars Climate Orbiter was lost in 1999 because one team worked in pound-force seconds and another in newton seconds. The arithmetic was correct throughout.
How does correct arithmetic destroy a spacecraft?
Step 2: Find Out
Isolate the amount and read the scale to the precision the instrument actually offers.
Step 1 — Predict
Why did the Mars Climate Orbiter fail?
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.
SI has seven base units
Meter, kilogram, second, ampere, kelvin, mole and candela. Everything else is built from them.
Prefixes are powers of ten
Kilo, centi, milli, micro. Conversion is a shift of the decimal point.
Units cancel like algebra
Carry them through and whatever survives names the answer.
Which catches errors the numbers cannot
A speed that comes out in kilograms means the equation was wrong, not the arithmetic.
A number without a unit is not a measurement
"The mass is 5" means nothing until you say grams or kilograms. Units are part of the value, and dropping them has caused spacecraft to be lost.
Prefixes are powers of ten
Kilo is a thousand, centi a hundredth, milli a thousandth, micro a millionth. Because everything is a power of ten, conversion is a shift of the decimal point rather than an arbitrary factor.
Step 4: A Common Mistake
Lots of people think
“Units are labels you add at the end.”
Step 5: Why the Kilogram Stopped Being a Lump of Metal
The same idea somewhere new.
Until 2019 the kilogram was defined by a platinum-iridium cylinder in a vault near Paris, and every kilogram on Earth was defined by that one object — which was slowly losing mass for reasons nobody fully established. It is now defined through the Planck constant, so any suitably equipped laboratory can realize it independently. All seven SI base units are now defined by constants of nature rather than by artefacts.
Step 6: Think It Through
Practice makes it stick.
The Lost Orbiter
Problem 1 of 2
The arithmetic was correct throughout. What went wrong?
The Wrong Units
Problem 2 of 2
A speed calculation comes out in kilograms per second. What does that tell you?
Number and Unit
1 of 5
How many SI base units are there?
2 of 5
250 ml in liters?
3 of 5
Why carry units through a calculation?
4 of 5
What defines the kilogram now?
5 of 5
90 km in 45 minutes, in m/s?
Step 7: Quick Check
Show what you know.
Question 1 of 1
Are units just labels added at the end of a calculation?
Step 8: Explain It in Writing
Claim, evidence, then reasoning.
The question
Explain why carrying units through a calculation catches errors, using the Mars Climate Orbiter.
Fill in all three boxes. The reasoning box is the one that matters most.
What You Found Out
- A measurement is a number and a unit together.
- SI has seven base units and prefixes that are powers of ten.
- Units cancel algebraically, and the survivors name the answer.
- Unit checking catches errors that correct arithmetic hides.