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Another Peek Beyond the Point

Sharing that never ends

Divide 5 by 11. The digits never stop: 0.4545454545 and so on.

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Start with the remainder 5. Share it by 11.
Step 1 of 4
  1. Start with the remainder 5. Share it by 11.
  2. Make it 50. 50 ÷ 11 = 4, remainder 6. The digit is 4.
  3. Make it 60. 60 ÷ 11 = 5, remainder 5. The digit is 5.
  4. The remainder 5 is back. So the digits 4, 5 repeat.

The rule

A remainder is what is left after sharing. A remainder is always less than the divisor. With divisor 11, only 0 to 10 can appear. Only 10 of them are above 0. The starting remainder counts as one of them. So after 10 digits, a remainder is 0 or has come back.

Either a remainder is 0 and the division ends. Or one comes back and the digits repeat.

The digits that repeat are the repeating block. For 5 ÷ 11 the block is 45.

Three divisions that never end
SumRemainders after each digitRepeating block
4 ÷ 944
5 ÷ 116, 545
3 ÷ 72, 6, 4, 5, 1, 3428571

Divisor 7 allows only the remainders 1 to 6. So its block has at most 6 digits.

Jump to lesson

This track

  1. 0 Start here
  2. 1 Times ten
  3. 2 Share into ten
  4. 3 Times a whole number
  5. 4 Times a decimal
  6. 5 A smaller answer
  7. 6 Sharing a decimal
  8. 7 Two names again
  9. 8 Decimals at work
  10. 9 Dividing by a decimal
  11. 10 Dividing by less than 1
  12. 11 Sharing that never ends
  13. 12 Checkpoint
  14. 13 The big picture
  15. 14 Track quiz

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