Eleventh Grade · Science · week 1

Measurement, Units, and Significant Figures

Convert between units using dimensional analysis and report calculated results with the correct number of significant figures.

Physics is the science of measuring the physical world and finding the patterns hiding in those measurements. Nearly every idea this year rests on the same starting point: a number is meaningless in physics until it is attached to a unit. Saying a car's speed is "60" tells you nothing -- 60 miles per hour and 60 meters per second describe very different cars. This year we work almost entirely in SI units (the International System): meters (m) for length, kilograms (kg) for mass, and seconds (s) for time, with every other unit -- like meters per second, or newtons -- built out of those three.

Two habits keep your numbers honest. The first is dimensional analysis: converting between units by multiplying by conversion factors written as fractions equal to 1 (like 1000 m / 1 km), canceling the unit you do not want and leaving the one you do. The second is significant figures ("sig figs"): the digits in a measurement that are actually known with confidence. A measuring tool never gives infinite precision, so a calculated answer is only as precise as the least precise measurement that went into it -- copying ten decimal places off a calculator does not make a measurement more true.

📋 For the teacher
Teach it (10–15 min):
  • Hand over an actual ruler, a kitchen scale, and a measuring cup, and measure five real objects together -- a shoe, a book, a cup of rice. Read each tool only to the precision it honestly offers, and talk about how many sig figs that measurement deserves.
  • Make the conversion-factor trick concrete: write a fraction like 1000 m / 1 km and physically cross out the "km" in the numerator and denominator so the cancellation is visible on paper, not just something you say out loud.
  • When multiplying or dividing measurements, have them count the sig figs in EACH input first and circle the smaller count -- that circled number is how many sig figs belong in the final answer, no more.
  • Keep a running joke about the "9.99999999 calculator answer": ask "does your ruler actually know that many decimal places?" to build the sig-fig instinct early, since it matters for every unit this year.
Talk about it:
  • Why is a unit as important as the number attached to it?
  • Why can a calculated answer never be MORE precise than the least precise measurement that went into it?
  • Where in daily life have you seen a measurement given with an unreasonable number of digits (too precise or too vague)?

Mastery looks like: They convert confidently between metric units using conversion factors and round a calculated answer to the correct number of significant figures without being reminded.

Common stumbles: Flipping a conversion factor upside down so the units do not actually cancel; copying every digit off a calculator screen regardless of how many sig figs the problem actually supports.

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