I never knew this fun fact ! I’ll try to use it with my students, and see if I this gets me more attention when I give them the trick to compute powers of 2 in your head (210 =~ 103, which leads to ln(103) =~ 10*ln(2) ).
For anyone wondering, the trick is : Powers of 2 below 10 are easy enough to remember or just compute in your head. So if you want to approximate 2x, write it as (210*a)*(2b), with a=x//10 (integer division) and b=x%10 (modulo). b will be 9 or less, so 2b is easy to compute, and 210*a = (210)a =~ 1000a is also easy to compute.
For instance, 232 = (230)(22). Since 230=~10003 ; and 22=4, then 232 =~ 4(1000)^3 = 4 billion. Once you get used to it, you’ll be able to say that 264 is approx 16 billion billions in no time ! :)
I never knew this fun fact ! I’ll try to use it with my students, and see if I this gets me more attention when I give them the trick to compute powers of 2 in your head (210 =~ 103, which leads to ln(103) =~ 10*ln(2) ).
For anyone wondering, the trick is : Powers of 2 below 10 are easy enough to remember or just compute in your head. So if you want to approximate 2x, write it as (210*a)*(2b), with
a=x//10(integer division) andb=x%10(modulo).bwill be 9 or less, so 2b is easy to compute, and 210*a = (210)a =~ 1000a is also easy to compute.For instance, 232 = (230)(22). Since 230=~10003 ; and 22=4, then 232 =~ 4(1000)^3 = 4 billion. Once you get used to it, you’ll be able to say that 264 is approx 16 billion billions in no time ! :)