1.3 Equality Test

It is better not to test equality in float point arithmetic. Just test if the difference is less than a specific small value i.e. 1e-8.

Bin2Dec(Dec2Bin(1.0, FALSE)) == 1.0

## [1] TRUE

Bin2Dec(Dec2Bin(1.1, FALSE)) == 1.1 # FALSE

## [1] FALSE

Bin2Dec(Dec2Bin(1.2, FALSE)) == 1.2 # FALSE

## [1] FALSE

Bin2Dec(Dec2Bin(1.3, FALSE)) == 1.3 # FALSE

## [1] FALSE

Bin2Dec(Dec2Bin(1.4, FALSE)) == 1.4 # FALSE

## [1] FALSE

Bin2Dec(Dec2Bin(1.5, FALSE)) == 1.5

## [1] TRUE

Bin2Dec(Dec2Bin(1.0)) == 1.0

## [1] TRUE

Bin2Dec(Dec2Bin(1.1)) == 1.1 # TRUE

## [1] TRUE

Bin2Dec(Dec2Bin(1.2)) == 1.2 # TRUE

## [1] TRUE

Bin2Dec(Dec2Bin(1.3)) == 1.3 # TRUE

## [1] TRUE

Bin2Dec(Dec2Bin(1.4)) == 1.4 # TRUE

## [1] TRUE

Bin2Dec(Dec2Bin(1.5)) == 1.5

## [1] TRUE

99/(72*1.3) == 99/72/1.3   # from Cockcroft-Gault Equation

## [1] FALSE

Explain the above result.