Repeating Decimal Decoder Game
Decode recurring decimal notation and reduce each repeating decimal to its simplest fraction.
Math puzzle challenges
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Instructions, device progress and accessibility
Choose Easy, Normal or Hard; use Practice or the shared UTC Daily seed. Enter answers on a keyboard or touchscreen, use Hint or Undo if needed, and press Check answer. Results save on your device when browser storage is available. Hints and Undo mark assisted rounds.
Local progress is checked when play begins.
How to play Repeating Decimal Decoder
Decode recurring decimal notation and reduce each repeating decimal to its simplest fraction. Start with Easy to learn the rules, then choose Normal or Hard for more steps. Work through every displayed value before pressing Check answer. Hints and Undo are available, but assisted rounds do not replace an unaided best score.
Math explained: Fractions & Decimals
Let x = 0.1666… . Then 10x = 1.666… and 100x = 16.666… . Subtract: 90x = 15, so x = 1/6.
Use the related calculators to practise calculations separately or verify the underlying mathematical method. The daily puzzle is deterministic for each UTC calendar day and difficulty; Practice creates new puzzles.
Worked example
Let x = 0.1666… . Then 10x = 1.666… and 100x = 16.666… . Subtract: 90x = 15, so x = 1/6.
Tips for improving accuracy
For a one-digit repeating block, use ninths. For two-digit blocks, use ninety-ninths, then account for any non-repeating prefix. Check dimensions and units as well as the number itself. The game works on desktops, tablets and phones without installing an application.
Frequently asked questions
What does the bar over a digit mean?
The overlined group repeats without end, for example 0.333… is written with a bar over 3.
Why must my answer be simplified?
Equivalent values are correct mathematically, but the puzzle asks for lowest terms; divide numerator and denominator by their greatest common divisor.