Welcome to the Digit Hotel

Imagine a hotel with four rooms in a row. From the right: the Ones room, the Tens room, the Hundreds room, the Thousands room. Every room has the same rule: it can hold at most 9 guests. That rule is the whole secret of how we write numbers.

Say 7 guests are in the Ones room and 2 more arrive. That makes 9. Fine. One more arrives: 10 guests. Too many! So all 10 hold hands, walk next door into the Tens room, and become one guest there. One ten. The Ones room is empty again. That is why we write ten as 1 0: one in the Tens room, nobody in the Ones room.

Now read 4 362 like a hotel manager. Thousands room: 4 guests, worth 4 000. Hundreds room: 3, worth 300. Tens room: 6, worth 60. Ones room: 2, worth 2. Add the rooms up and you get the number. A digit is never just itself; it is the digit times its room.

What about an empty room? In 7 049 the Hundreds room has nobody in it. We still have to write the room down, or the digits slide into the wrong rooms and 7 049 turns into 749. That is the job of zero: it holds a place. Zero is the most important guest in the hotel, and it is not even there.

Ten thousands rooms is where this hotel stops for now. 9 999 is every room full. Add one more guest and the whole hotel regroups, room by room, into a brand-new fifth room: 10 000. Grade 4 works up to there. Next year, the hotel gets bigger.