Chapter 2 · Measurement and Problem Solving

2.1The Metric Mix-up: A $125 Million Unit Error

8 min · two checks

Predict

Can a correct formula still destroy a spacecraft?

The idea

Explain why a unit is part of a quantity, not a label you add at the end.
State the lesson of a famous metric–imperial mismatch.

A measured quantity is a number times a unit. Strip the unit off and the number no longer refers to the same amount. 5 without a unit might be seconds, grams, or kilometers. Teams that exchange numbers without agreeing on units are not exchanging measurements. The Mars Climate Orbiter was lost in 1999 after thrust data produced in pound-force seconds were used as if they were newton-seconds. The factor between those units is about 4.45, large enough to push a trajectory into the atmosphere.

That failure is why this chapter is fussy. Every conversion will show the unit that cancels. Every answer will wear a unit. “The calculator said 12” is not a result until you can say 12 of what, and why that size makes sense.

Keep these

A quantity is a number and a unit together.
Unit mismatches scale the real world, not just the homework.
Show cancellations. Do not attach a unit after the fact.

Check yourself

1. Two groups report the same reading as “250” but one means newtons and the other means pounds-force. The numbers match, so

the forces are equalthe forces differ by the conversion factor between those unitsunits never affect engineeringscientific notation would have prevented any difference

2. The practical rule from the orbiter loss is

avoid the metric systemtreat units as part of the calculation and make them cancel on the pageround earlier so units matter lessonly convert at the end, in your head