Number Systems: Notation, Not Property
Tier 1 separated three things most people fuse: the number in the cell, its meaning (the agreement), and — mentioned once, promised a lesson — its spelling. Today the third layer gets its lesson. "13", "1101" and "D" look like three different things; by the end of this page they are one number in three coats, and the words "binary" and "hexadecimal" stop being magic and become wardrobe.
Learning goals: state the positional principle with the base as a parameter; convert small numbers between notations as a retelling, by hand; and collect the payoff owed since the fractions lesson — why 0.1, exact on paper, is approximate in the machine.
The positional principle: base as a parameter
What does the record "13" actually say? Not "one-three" as a picture — it says: 1 ten and 3 ones: 1×10 + 3. Each position is worth a power of ten, each digit says how many of that power. Now the move that opens everything: ten is not sacred. It is a parameter — the base — and any whole base from two upward runs the same machinery: