Formula Round(4.975, 0.01) getting 4.97, expecting 4.98

[Yongcan]

Hi All

Today's we notice one odd behavior of Round function. 

Formula Round(4.975, 0.01) getting 4.97, is it should be 4.98? can't figure out why and also the behavior of select tool is same.

[Yongcan]

notice once I change the number to string format then use select with fixedDecimal then i get the expect result. things getting interested now.

[danilang · Accepted solution]

Hi there @Yongcan 

You've stumbled across one of the deep problems with floating point representation.  As I'm sure you know, integers are held in binary and can be exactly represented.  0101 = 5, 0110 = 6, etc. However, floats are stored in 3 parts

1 sign bit

8 exponent bits  

23 Mantissa bits

The mantissa is the closest value of the series 1*(1/2) + 0*(1/4) + 1*(1/8) + 0*(1/16) +………+ 0*(1/2^23) = 0.625.   

Some decimals are exactly represented

0.5=(1*(1/2) + 0*(1/4))

0.25(0*(1/2) + 1*(1/4))

0.75(1*(1/2) + 1*(1/4))

The problem arises because not all decimals can be exactly represented by this series. 0.1 is one particularly vexing example.  As you can see in the table, the expansion of 0.1 is actually 0.10000000000000001 

These results were generated using the following formulas

The Fixed17 column gives an approximation of how the number is represented internally

What's troubling about these results is that the round() function and the conversion to 19.2 don't give the same results suggesting that there are 2 different rounding mechanisms in place.  I think you should open a ticket to have this addressed.

But how to solve your problem. If you add a small amount to each number before rounding you'll get consistent results.  The small amount should be several orders of magnitude smaller than what your round to, but several orders larger than the internal representation.  In my RoundPlusSmall formula I used

round([Number]+0.00000001,0.01)

Dan

[dynamicsnail]

We just stumbled across this problem and are wondering if anyone ever opened a ticket to have it addressed?