Tuesday, January 14, 2014

[ekrneufq] Base 7

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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