In contrast to, say, base 30, base 7 has very few terminating decimal expansions because it is a prime number.
1/2 | 0.333... |
1/3 | 0.222... |
1/4 | 0.15 15 15... |
1/5 | 0.1254 1254 1254... |
1/6 | 0.111... |
1/7 | 0.1 |
1/8 | 0.06 06 06... |
1/9 | 0.053 053 053... |
1/10 | 0.0462 0462 0462... |
1/11 | 0.0431162355 0431162355 0431162355... |
1/12 | 0.04 04 04... |
1/13 | 0.035245631421 035245631421 035245631421... |
1/14 | 0.0333... |
1/15 | 0.0316 0316 0316... |
1/16 | 0.03 03 03... |
1/17 | 0.0261143464055232 0261143464055232 0261143464055232... |
1/18 | 0.025 025 025... |
1/19 | 0.024 024 024... |
1/20 | 0.0231 0231 0231... |
1/21 | 0.0222... |
The next terminating fraction is 1/49.
Base 2, 3, or 5 would be just as bad, but seemingly less weird than 7.
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