how to generate auto number from 0,000000000000000000000000000001 till 0,999999999999999999999999999999 at excel and the format cell is number ?
i've tried for dragging mouse , but i guess thats so terrible
You're out of luck.
Excel uses a 64 bit double precision IEEE754 floating point type for numbers (along with some clever rounding tricks). That gives you 53 bits of precision which loosely translates to 15 decimal significant figures of accuracy.
You will not be able to descriminate between numbers with such a small interval between them, if the total range is between 0 and 1.
(There's also the small matter of there not being enough space in a workbook to represent all those numbers.)
Related
We have some weird calculation scenario in Microsoft excel, this simple addition operation resulting 1 at 13 decimal digit whereby it should be zero
But when i extract the value in formula the result is correct (both formula value is the same but the result is different)
From human understanding addition calculation will reduce the decimal digit rather than add it.
Is this by design or bugs ?
I strongly guess that this is a gap from the limited precision of floating point numbers. Accuracy of digital numbers is limited. Numbers in excel are saved in binary format(but displayed in decimal format). This means that the "0" is not as protected as in the decimal system. Usually Excel tries to cover this up for examples like yours.
Also, if your numbers derive from complex calculations (e.g. square-roots), the accuracy can be limited as most functions use approximation with limited iterations to give a result.
You can find more information about floating point arithmetic here. The blog is about pythin but the way it works is similar.
https://docs.python.org/3/tutorial/floatingpoint.html
How does excel determine what to number to display? specifically the number of decimal places
for example:
50.98, when stored as a single-precision float is 50.979999542236328125
50.979999 is also stored as the exact same single-precision float
(binary rep. 01000010010010111110101110000101, taken from here: https://www.h-schmidt.net/FloatConverter/IEEE754.html)
when i type 50.98 & 50.979999 into 2 cells, change format to number, and extend out the decimal places using the formatting button
it represents them exactly as 50.98 & 50.979999, as i originally typed.
how is that working? is excel storing the exact text i typed and not (directly) storing the float data type at all?
if it stores it as a double, how does it preserve the exact precision i originally typed in that case?
i can't find documentation outlining how this works.
Note its not causing me any problems, i just need an explanation for differences in how excel displays vs calculations based on those values.
it represents them exactly as 50.98 & 50.979999, as i originally typed.
Excel is padding with zeros after 15 significant decimal digits.
The internal number is encoded with a high enough binary precision such that limiting output to 15 deimcal places, the original typed in decimal values appear to be exactly that.
=2/3 is an informative example showing this limit and exposing the binary internals by carefully extracting out a bit at a time.
As displayed in one cell, decimal output rounds to 15 places, padding with zero after that.
0.66666666666666700000000
The below does a binary conversion of =2/3 and forms 0.101010101010101010101010101010101010101010101010101012, exactly what is expected if Excel used a binary64. (Below)
OP's observations are consistent with using binary64 and rounding output as decimal text to 15 significant digits.
Cell A3: =FLOOR(B2*A$1,1), Cell B3 = =B2*A$1 - A3
Hypothesis: When displaying a number, Excel first converts a number to a decimal numeral with at most 15 significant digits even if more are requested. If additional digits are requested, they are filled in as zeros. (In addition, Excel may apply other alterations depending on context.)
In Microsoft Excel 2008 for Mac, I entered =1+22*POWER(2,-52) in A1 and =1+23*POWER(2,-52) in A2. Using IEEE-754 binary64, these should generate the numbers 1.000000000000004884981308350688777863979339599609375 and 1.0000000000000051070259132757200859487056732177734375. Entering =A1-1 and =A2-1 in B1 and B2 and setting these to Number format with 30 decimal places shows “0.000000000000004884981308350690” and “0.000000000000005107025913275720”, which is consistent with IEEE-754 binary64. So we have some assurance the numbers above were indeed generated and stored in Excel.
Setting A1 and A2 to Number format with 20 decimal places shows “1.00000000000000000000” and “1.00000000000001000000”.
Clearly, if Excel were displaying the actual numbers with 20 decimal places, it would show “1.000000000000004885” and “1.000000000000005107”. It does not. The display we see is consistent with converting the numbers using 15 decimal digits (significant digits, not just those after the decimal point) and then padding with zeros.
Converting 50.98 to the IEEE-754 binary64 format yields 50.97999999999999687361196265555918216705322265625. Displaying this with 15 decimal digits yields 50.9800000000000.
A colleague of mine sent me their Excel sheet and asked me to take a look at it. The issue is that with a very specific number (56136.598), Excel is automatically extrapolating that number out to 10 decimal places completely regardless of the formatting options.
The cell displays the number to the correct 3 decimal places, but if you look at the number in the formula bar it displays all 10 decimal places. It even changes the number to 10 decimal places if I write the formula =round(56136.598,3) to =round(56136.5979999999,3).
Unfortunately, given the industry I am in, I need some explanation as to why this very specific number induces this change. It's not enough to just use a round or trunc function to lop it off at 3 decimal places, the fact that this number and this cell have a different set up then the rest of the parallel cell calculations is drawing some criticism. Has anyone ran into this before? I have tried it in Excel 2010 and 2019 and in new worksheets, same issue. It seems that excel refuses to accept the number at 3 decimal places and forcing an expansion to 10 decimal places on its own.
This is a normal behavior. See the image below where I just entered 56136,598 into the cell.
This happens due to the fact that Excel is a numeric calculation program and not an algebraic one. So it is a problem of precision. Also see Numeric precision in Microsoft Excel.
Excels results are not absolute but very close to correct. The difference between these to numbers is almost 0 (the difference is 0,0000000001).
And this is actually how most common calculators will act too (you just don't see that). It is just the nature of how calculators (and computers) work.
So there is nothing to worry about.
More about this: Understanding Floating Point Precision, aka “Why does Excel Give Me Seemingly Wrong Answers?”
A friend of mine discovered a really weird thing in MS Excel. Excel rounds down some specific numbers the wrong way, actually it rounds down a number that shouldn't need rounding.
As far as I have tested, it happens in most versions of MS Excel 2007+
Eg. the number 10358.165790 will be rounded down to 10358.1657899999.
Apparently it only happens in this interval: 8192.165790 - 65535.165790.
It is really weird - it doesn't happen with eg. .165890 or .165690, only with .165790.
Do any of you know why this happens and why it only accounts to certain numbers?
Excel uses an IEEE754 64 bit double precision floating point type to represent numeric data; with some clever formatting and roundup tricks to get sums like 1/3 + 1/3 + 1/3 correct.
What you are observing is a natural consequence of that numeric scheme only being accurate to 15 significant figures. Unless the number happens to be a dyadic rational, in which case it can be stored exactly, the closest representable number is chosen to the one you actually want. This may be below or above a rounding cutoff.
It will occur in other ranges other than the one you cite too.
I've got an Excel sheet which is exhibiting strange behaviour. I have 2 values, followed by an average of those 2 values - simple enough, right?
However, if I change the number format of the top cell from 2 decimal places to 30, I get a different result:
Can anyone explain this? When a cell is formatted to 2 decimal places, does that mean all formulae using this cell are rounding the value to 2 decimal places also?
Check your Excel options (Alt+F,T) for the Advanced ► When calculating this workbook ► Set precision as displayed option. When this is checked, calculation is automatically rounded off to the displayed number of decimals rather than the internal 15 digit floating point precision. It also permanently truncates the raw value to the displayed precision so I am unclear on how you are bouncing between the two average values.
The actual average of 1.6786427146 and 1.73 is 1.7043213573 which is 1.70 when only two decimals are displayed. It would only be through Precision as displayed that 1.6786427146 would actually be converted to 1.68 making the average 1.71.
Turn the option off and the underlying raw value will be stored to a 15 digit floating point precision. The same goes for all internal formula calculations.