Difference between revisions of "142857"
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| − | The number ''142857'' has the curious property that, if it is multiplied by any number from 1 to 6, the result is a number with the same digits in the same order (a cyclic permutation). | + | The number ''142857'' has the curious property that, if it is multiplied by any number from 1 to 6, the result is a number with the same digits in the same order (a [[cyclic permutation]]). |
For example, 142857 × 3 = 428571. | For example, 142857 × 3 = 428571. | ||
| Line 6: | Line 6: | ||
:1/7 = 142857/999999 | :1/7 = 142857/999999 | ||
| − | and that 1/7 expressed as a decimal is | + | and that 1/7 expressed as a [[decimal]] is |
:0.142857142857142857142857142857... | :0.142857142857142857142857142857... | ||
| − | Investigating the number 142857 can lead a student into an understanding of repeating decimals and rational numbers. | + | Investigating the number 142857 can lead a student into an understanding of repeating decimals and [[rational numbers]]. |
[[Category:Mathematics]] | [[Category:Mathematics]] | ||
Revision as of 01:21, March 15, 2007
The number 142857 has the curious property that, if it is multiplied by any number from 1 to 6, the result is a number with the same digits in the same order (a cyclic permutation).
For example, 142857 × 3 = 428571.
This property is closely related to the facts that
- 1/7 = 142857/999999
and that 1/7 expressed as a decimal is
- 0.142857142857142857142857142857...
Investigating the number 142857 can lead a student into an understanding of repeating decimals and rational numbers.