Lesson 2 — Number Systems & Place Value
Before any explanation, try these. Each one is about what a digit is really worth depending on where it sits.
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Place value: where a digit sits decides what it means
Our everyday number system is base-ten: we have ten digits (0–9), and each place is worth ten times the place to its right. The same digit means different amounts in different places.
| Thousands | Hundreds | Tens | Ones |
|---|---|---|---|
| 4 | 7 | 2 | 8 |
In 4,728 the 7 is not "seven" — it sits in the hundreds place, so it is worth 700. This is exactly what base-ten blocks make visible in a classroom: a single cube is one, a rod is ten ones, a flat is ten rods (a hundred), and a big cube is ten flats (a thousand). "Carrying" and "borrowing" are just trading ten of one block for one of the next.
Why ten? And what if it were two?
There is nothing magic about ten — it is almost certainly because we have ten fingers. A place-value system can be built on any base. Computers use base-two (binary): only two digits, 0 and 1, and each place is worth twice the place to its right (1, 2, 4, 8, 16, …).
Reading binary 1101: (1 × 8) + (1 × 4) + (0 × 2) + (1 × 1) = 13.
The big idea transfers: in any base, a digit's value is the digit times the value of its place. Understanding that is what makes place value a concept and not just a memorised lineup of columns.
Sets and logic: the language underneath
A set is just a collection of objects — for example, the set of even numbers, or the set of digits {0, 1, 2, …, 9}. Two ideas come up constantly:
- Union (∪): everything in either set. {1, 2} ∪ {2, 3} = {1, 2, 3} — list each element once.
- Intersection (∩): only what is in both sets. {1, 2} ∩ {2, 3} = {2}.
Simple logic words ride along with sets: and matches intersection, or matches union. "Numbers that are even and less than 10" is an intersection; "even or less than 10" is a union.
True or false? You decide
Decide whether each statement is true or false. Instant feedback either way.
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Quick check
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