We aim to perform calculation with 100% accuracy.
Every calculator that doesn't simplify the expression has some inaccuracy. Simply because some intermediate values in calculation require infinite precision when stored in decimal form.
For example, √5×√5 equals exactly 5 but how a typical calculator evaluates it is:
√5 : 2.23606797749979
So, √5×√5 = 2.23606797749979×2.23606797749979
= 5.000000000000001
Although it gets rounded off and what you see is 5, you can check it as:
- (√5×√5 - 5) doesn't give 0 in Microsoft Calculator
- 1/(√11×√11 - 11) results in calculation timeout instead of zero division error in Realme Calculator
This was only to give you an idea of what we are aiming at.
Scientific Calculators do simplify the expression and I have not found any inaccuracy in them till now.
Inaccuracy in rational decimals is easy to get rid of by handling them as fractions. So the real quest for us is handling irrationals!