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Science · Honors Chemistry

Chapter 1: Quantitative Foundations

Advanced Dimensional Analysis

A conversion factor is a way of writing one.

Lesson
2
Time
About 25 minutes
Practice
Using mathematics and computational thinking
Crosscutting concept
Scale, proportion, and quantity
Core idea
PS1.A: Structure and Properties of Matter

The Unit That Did Not Cancel

In September 1999 Mars Climate Orbiter was lost at Mars. One team’s software reported thruster data in pound-force seconds, and the navigation software read them as newton-seconds.

Every number was correct in its own unit. What kind of check would have caught the error?

Page 1

Make your guess to turn the page.

Still to come: 11 pages · Lab · Words to Know · What We Learned · 4 questions · Explain It in Writing · Open Questions

For the grown-up

The idea this lesson is working on — Students memorize, for each conversion, whether to multiply or divide. The book treats every factor as a fraction equal to one, with the unwanted unit in the denominator, so the direction is never a choice. Ask: which unit do you want to cancel, and where must it go? The idea to reach is that canceling units both converts and checks.

The orbiter, and the lab’s link to lesson 1 — The investigation board’s Phase I report came out on 10 November 1999. The altitude figures are the board’s estimates and are rounded here. The lab’s widget is the significant-figure one, so the book uses it to show that exact conversion factors never change the figures a measurement justifies. Its readout labels the first instrument a "meter stick"; the book says meter stick.