The fuses and switches you see follow the R10 Renard series. This series of 10 numbers (1.00, 1.25, 1.60, 2.00, 2.50, 3.15, 4.00, 5.00, 6.30, 8.00), for each order of magnitude, provides an approximately-equal geometric spacing for ten component values per decade.
Why geometric spacing, and not, say, equal arithmetic spacing between successive values (e.g. 2, 4, 6, 8, 10)? It comes down to the tolerance and error allowance for each component. For R10 specifically, each value is about 1.26 times the previous value; a manufacturing process that provides a 15% tolerance can't actually make its nominally-valued components more precisely than this anyway. You might want a 117 A breaker, but any given 125 A ± 15% breaker might actually trip at 117 A (or 143 A) anyway. Better to design a system such that you know the breaker will trip before damage occurs -- either by using your 125 A breaker with components that can tolerate 150 A, or by using a 100 A breaker with your 117 A load.
Conversely, if we did use the 2, 4, 6, 8, 10 series, we'd have a mismatch: 50% tolerance in the first gap, but only 12% tolerance in the final gap. This is not particularly useful -- either the manufacturing process results in 50% tolerance and there's a lot of overlap at the higher digits, or the process can do 12% tolerance and some of the range is not covered.
A related concept is the E series of preferred numbers that you may have seen on resistors and capacitors. Capacitors with 20% tolerance usually come in the E6 range; brown four-stripe (5%) resistors frequently come in hobbyist starter kits following E12, and the blue ones match E24 or E48.
These "preferred number" patterns are everywhere. Convenient multiples across orders of magnitude are found in electronics, yes, but also (for example) in currency denominations. American 1¢, 5¢, 10¢, 25¢, 50¢, $1, $2, etc. follows this idea unevenly, but other (more sensible) currencies like the Australian dollar or the Euro follow a 1-2-5 pattern consistently. You can typically buy milk (or other groceries) in 0.25 L, 0.5 L, 1 L, 2 L, and 4 L. The A-series of paper sizes (e.g. A4) are each half the previous number's size. In photography, camera aperture F-stops and ISO film speeds both fit the bill. I'm sure you'll start seeing them everywhere.
It turns out it's really useful to say "I need the next one to be X% bigger" and these patterns just fall out of there.
(Addendum, the math):
Specifically for R10, the values are approximately \$10^{n/10}\$, where \$n\$ is an integer between 0 and 9. The values are then rounded for convenience.
| Value |
Nominal |
Exact |
| 1 |
1 |
1.000 |
| 2 |
1.25 |
1.259 |
| 3 |
1.6 |
1.585 |
| 4 |
2 |
1.995 |
| 5 |
2.5 |
2.512 |
| 6 |
3.15 |
3.162 |
| 7 |
4 |
3.981 |
| 8 |
5 |
5.012 |
| 9 |
6.3 |
6.310 |
| 10 |
8 |
7.943 |
Any \$n\$-step evenly-spaced geometric sequence can be calculated using the general formula
$$ n^{(i-1)/n} $$
where \$n\$ is the number of steps, and \$i\$ is an integer between \$1\$ and \$n\$ inclusive.
