Opening Lilerno
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Lesson 01 · Begin here
Before we design a machine, let’s learn to describe a single part.
Imagine asking someone to cut a piece of material “120 long.” They still don’t know what to cut. A number becomes a useful measurement when you attach a unit.
| What you measure | SI base unit | Symbol |
|---|---|---|
| Length | metre | m |
| Mass | kilogram | kg |
| Time | second | s |
SI has seven base units in total; these three are enough for today. Millimetres and centimetres express fractions of a metre. Mass is not weight: weight is a force, which we will study later.
Write the unit every time. “Length = 120 mm” is a useful statement. “Length = 120” is incomplete.
Suggested pace: 20–30 minutes, plus later recall. This is a study estimate, not academic credit.
Save your place when you finish reading.
A centimetre contains 10 millimetres. A metre contains 100 centimetres, or 1,000 millimetres. The same part can have a different number on its label.
Dividing by 10 makes a number one tenth as large. Dividing by 1,000 makes it one thousandth as large: 120 ÷ 1,000 = 0.120 = 0.12. Multiplying reverses the operation.
A fraction with equal quantities on top and bottom has the value 1. Multiplying a measurement by that fraction changes its units without changing what it describes.
120 mm is not 120,000 m. When you choose a larger length unit, the number gets smaller. The part itself stays exactly the same.
250 ÷ 1,000 = 0.25 m, a quarter of a metre.
Units participate in multiplication and division just like numbers. That is why length, area, and volume cannot use the same conversion factor.
A superscript 2 means “multiply this by itself.” The top of a 40 mm by 20 mm block has an area of 800 mm². To express it in cm², convert both lengths.
A superscript 3 means three factors. A 20 × 10 × 10 mm block is also a 2 × 1 × 1 cm block.
If a carriage travels 0.6 m in 3 s, its average speed is the total distance divided by the elapsed time. It need not move at a constant speed during the whole trip.
Distance × time gives m·s, not m/s, so it cannot be a speed. Matching units can catch errors, but cannot prove a formula is correct: a wrong numerical factor can still have the right units.
The block model uses exact chosen dimensions. A real ruler has limited resolution. Extra calculator digits do not make a measurement more accurate. We will study uncertainty and significant figures in the measurement chapter.
Use paper if it helps. Explain your method before checking. All five correct answers complete this lesson’s checkpoint; you can retry as often as you need.
Loading your recall practice…
Algebra for physical problems: if speed = distance ÷ time, how do you find the time? Build that reasoning from simple arithmetic.
Continue to algebra →Measure the length and width of a book with a ruler. Record the units, sketch its top face, and calculate its approximate area. Express the result in both cm² and mm². Explain why those numbers differ.
Open learning, traceable sources
Original Lilerno lessons and diagrams, supported by these references. Free access does not always permit republication. Links open the publisher’s material.
Lesson 01: SI units, prefixes, and quantity notation.
CC BY 4.0; cited as a factual reference. No figures reproduced.
Open source ↗Rights / publisher record ↗Arithmetic, fractions, powers, and the bridge to algebra.
Reference only. Verify the current book and asset licence before reuse.
Open source ↗Rights / publisher record ↗Lesson 01: unit conversion and physical quantities; broader mechanics and electricity reading.
CC BY-NC-SA; reference only. No text, questions, or figures reproduced.
Open source ↗Rights / publisher record ↗Optional tool for opening the original parametric part exported by lesson 01.
Tool: GPL v2. Lilerno supplies its own original model; no tool code is embedded.
Open source ↗Rights / publisher record ↗