If you divide a square of unit area into 2 equal parts, each will have a value of 0.5.
By dividing one of these into 2 equal parts and continuing
to dissect in the same way, the values will be obtained: 0.5; 0.25; 0.125; 0.0625;
0.03125; ...
In other words, a geometric series is obtained whose
sum converges to 1:
A scale with available weights: 0.5 lb; 0.25 lb; etc., could measure any object less than 1 pound. What we are doing is using a numbering system based on 2.
Probably everyone has tried their hand at binary numbers, but few people will have used this base to deal with decimals, here we propose an example:
3,14159265358979323846… = 11,00100100001111110110101...
The whole part will probably be clear to everyone,
while the other part will require a minimum of reasoning.
These tables can perhaps help:
Here are some examples of pi in various numbering systems.
As an exercise, you can see how simple the transition from base 2 to base 4 and from base 4 to base 16 is.base-2 (binary code) : 11.0010010000111111011010101000100010000101101000110000100011010011000100110001100110001010001011100000
…
base-4 : 3.0210033312222020201122030020310301030121202202320003130013031010221000210320020202212133030131000020 …
base-16 (exadecimal code): 3.243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89452821E638D01377BE5466CF34E90C6CC0AC …
base-3 : 10.0102110122220102110021111102212222201112012121212001211001001012220222120120121112101210112002201202
...
base-5 : 3.0323221430334324112412240414023142111430203100220034441322110104033213440043244401441042334133011323 ...
base-6 : 3.0503300514151241052344140531253211023012144420041152525533142033313113553513123345533410015154344401 ...
base-7 : 3.0663651432036134110263402244652226643520650240155443215426431025161154565220002622436103301443233631 ...
base-8 : 3.1103755242102643021514230630505600670163211220111602105147630720020273724616611633104505120207461615 ...
base-9 : 3.12418812407442788645177761731035828516545353462652301126321450283864034354163303086781327871588 ...
Zibaldone
Scientifico: pi (zibalsc.blogspot.com)
