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REPEATING DECIMALS

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REPEATING DECIMALS

which fractions stop, which run for ever, and how to know the length of the repeat without dividing

Built as a memo rather than a table: the thing worth hanging it up for reads across the room, with the full reference in smaller type below it.

Three sizes in one archive — from a sheet on the fridge to a poster on the wall.

StandardUS$1.50

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Formats
A4 · A3 · A2
What you get
Print-ready PDFs, one per size, with every letterform converted to outlines — nothing to install, nothing to shift.
Subject
maths · school · reference · study

The brackets mark what repeats: 0.1(6) reads as "nought point one, then sixes for ever". The number in a cell is the length of the repeat in digits; "STOPS" means the decimal is finite. The rule under a cell marks the denominators that repeat.

WHY A COMPUTER DOES NOT KNOW ONE TENTH

The rule is the same in any base, and it is why a computer cannot write down one tenth exactly. In base two only fractions whose denominator is built from twos stop; ten has a five in it as well, so one tenth repeats in binary exactly as one third repeats in decimal.

Hence the familiar oddity: 0.1 + 0.2 comes out as 0.30000000000000004, not 0.3. Nothing is broken — that is an endless expansion rounded to a finite number of bits, twice over. It is also why money is counted in whole cents rather than in fractions of a unit.

On the sheet

  • The brackets mark what repeats: 0.1(6) reads as "nought point one, then sixes for ever". The number in a cell is the length of the repeat in digits; "STOPS" means the decimal is finite. The rule under a cell marks the denominators that repeat.
  • Colour carries meaning, but meaning never rests on colour alone — the sheet reads in black and white.
  • Nothing about how it was made: the sheet carries only what the reader needs.

Printing

  • Three sizes in the archive: A4 — 210×297 mm, A3 — 297×420 mm, A2 — 420×594 mm.
  • All text is converted to outlines. No fonts to install, and nothing shifts on another machine.
  • White background and sparing fills — it prints on a home printer without draining the cartridge.
  • Margins of at least 10 mm: a home printer cannot print to the edge.
  • No stroke thinner than 0.3 mm, so nothing disappears in print.

Why the numbers can be trusted. Every countable number here is computed from data rather than typed in, and the sheet must pass 8 independent checks before it is allowed to build — how many items there are, the order they come in, and the claim in the highlighted box itself. If one fails, there is no file.

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