Solution 1.1:7d
From Förberedande kurs i matematik 1
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There is, admittedly, a repeating pattern in the decimal expansion | There is, admittedly, a repeating pattern in the decimal expansion | ||
| - | ::<math>0 | + | ::<math>0\textrm{.}\underline{10}\ \underline{100}\ \underline{1000}\ \underline{10000}\ \underline{100000}\,\ldots</math> |
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| - | but for it to be a rational number, the decimal expansion must, after a certain decimal place, consist of a combination of digits that repeat themselves indefinitely. There is no such repetition in the | + | but for it to be a rational number, the decimal expansion must, after a certain decimal place, consist of a fixed combination of digits that repeat themselves indefinitely. There is no such repetition in the decimal expansion given above (the digit groups 10, 100, 1000, 10000, ... increase in size all the time). The number is therefore not rational. |
| - | decimal expansion given above (the digit groups | + | |
| - | 10, 100, 1000, 10000, ...increase in size all the time). The | + | |
| - | number is therefore not rational. | + | |
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Current revision
There is, admittedly, a repeating pattern in the decimal expansion
- \displaystyle 0\textrm{.}\underline{10}\ \underline{100}\ \underline{1000}\ \underline{10000}\ \underline{100000}\,\ldots
but for it to be a rational number, the decimal expansion must, after a certain decimal place, consist of a fixed combination of digits that repeat themselves indefinitely. There is no such repetition in the decimal expansion given above (the digit groups 10, 100, 1000, 10000, ... increase in size all the time). The number is therefore not rational.
