Which is longer 5 miles or 10 kilometers?

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Answer 1 · 2016-11-03T23:21:14

$10$ kilometers

$5$ miles is about $8$ kilometers, so $10$ kilometers is longer.

The exact conversion figure is $1.609344$ , which follows from one inch being defined as $2.54$ cm

I find it handy to use the first few terms of the Fibonacci sequence as an approximation for converting between miles and kilometers.

The Fibonacci sequence starts $1, 1$ . Then every subsequent term is formed by adding the two previous terms:

$1, 1, 2, 3, 5, 8, 13, 21, 34,...$

The ratio of pairs of consecutive terms tends towards the Golden ratio $~~ 1.618034$ , which is not too far off $1.609344$ .

Hence we find $5$ miles is about $8$ kilometers, $8$ miles is about $13$ kilometers, etc.