More Digits Isn't Bigger

Where it usually goes wrong

"More digits, bigger number" is exactly right for whole numbers — 450 beats 50 — and it is carried straight into decimals without anyone flagging that the rule flipped: 0.45 has two digits after the point and 0.5 has one, and 0.5 is still the larger value, because a decimal's size is set by its LEFTMOST digits, not its longest.

Try this

• Press "0.45 vs 0.5". Count the shaded squares on each grid rather than the digits in each label — the blue grid, with the longer-looking number, is visibly less full.
• Drag the blue grid down to 0.4 and back up slowly, one row at a time. Each full row is one tenth — the FIRST digit after the point is the one worth the most, however many more come after it.
• Press "0.5 vs 0.50". Both grids fill to the exact same 50 squares — the extra zero changes nothing about the shading, which is what "equal, written to two depths" means.

Where this goes next

Ordering a list of decimals uses the same rule repeated: line every number up on its decimal point, pad the shorter ones with invisible trailing zeros, and compare one column at a time from the left — the column count was never the number to trust.