Different results from ruby floating-point expressions

Question

What is difference between Case 1 and Case 2?

I think the result should be the same: 7.78

Can someone explain to me?

Case 1： a=(x/y).round(4)*100

Case 2： a=(x/y*100).round(2)

Case 1

x=7.0 y=90 a=x/y => 0.07777777777777778 a=a.round(4) => 0.0778 a=a*100 => 7.779999999999999

Case 2

x=7.0 y=90 a=x/y => 0.07777777777777778 a=a*100 => 7.777777777777778 a=a.round(2) => 7.78

Duplicate of stackoverflow.com/questions/4055618/ruby-floating-point-errors — DevDude
– DevDude, Commented May 7, 2014 at 3:44

spickermann · Accepted Answer · 2014-05-07 03:49:36Z

Floating-point numbers cannot precisely represent all real numbers, and floating-point operations cannot precisely represent true arithmetic operations, this leads to many surprising situations.

I advise to read: https://en.wikipedia.org/wiki/Floating_point#Accuracy_problems

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