Lesson 11 of 15
Sharing that never ends
Show on a big screenDivide 5 by 11. The digits never stop: 0.4545454545 and so on.
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Step 1 of 4
- Start with the remainder 5. Share it by 11.
- Make it 50. 50 ÷ 11 = 4, remainder 6. The digit is 4.
- Make it 60. 60 ÷ 11 = 5, remainder 5. The digit is 5.
- 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.
| Sum | Remainders after each digit | Repeating block |
|---|---|---|
| 4 ÷ 9 | 4 | 4 |
| 5 ÷ 11 | 6, 5 | 45 |
| 3 ÷ 7 | 2, 6, 4, 5, 1, 3 | 428571 |
Divisor 7 allows only the remainders 1 to 6. So its block has at most 6 digits.
Try the lab to finish this lesson.