give the formula for calculating an irrational number between two rational
numbers?
Between 2.3 (which is the rational number 23/10) and 2.4 (which is the rational
number 12/6), you could give this irrational number, a never-ending decimal:
2.30100100010000100000100000010000000100000001.....
After the 2.3, put 1 zero then a 1, then 2 zeros then a 1, then 3 zeros then a
1, and so on. That number is irrational and it's between rational number 2.3
and rational number 2.4. You can do this given any two rational numbers.
Write the smaller rational number as a terminating decimal, then after its last
decimal place, put 1 zero, then a 1, then 2 zeros, then a 1, then 3 zeros then
a 1, on and on forever. That will be an irrational number which is between the two rational numbers.
Between rational numbers 5.768903 and 5.768904, there is this irrational
number:
5.768903010010001000010000010000001...
Between 73 and 74 there is this irrational number
73.010010001000010000010000001...
Edwin
