Do we need 15 decimal places?
Who needs 15 decimal places? The IEEE round off error were users get, say, 12.3 × E15 when they expect zero just confuses then and undermines their confidence in Excel and in themselves.
I cannot see any one in the finance world needing 15 decimal places.
Few, if any, engineers/scientist work with that sort of precision. Look up physical constants and you will find they are generally known to only 9 significant figures: Planck constant h = 6.626 070 040(81) × 10−34, were (81) is the std dev in the last two decimal places. Albeit some work with atomic masses of isotopes to 12 sig figs.
Suggestion: an option (on by default) to limit formats to 12 decimal places  generally the round off error disappears with =ROUND(formula,12)
6 comments

JoeU commented
I disagree with the suggestion. Generally, calculations should be rounded to the precision required, not to some arbitrary precision. Rounding to 12 decimal places does not hide rounding errors, in general. Two counterexamples....
Example #1:
A1: 34639.969
A2: 5.273
A3: =ROUND(A1A2,12)
A4: =ROUND(A1A2,3)
A5: =A334634.696=0
A6: =A434634.696=0A6 returns TRUE. But A5 returns FALSE because A3 is actually 34634.6959999999. (That is, the binary representaton of that constant.)
Example #2:
A1: 8234.558
A2: 8234
A3: =ROUND(A1A2,12)
A4: =ROUND(A1A2,3)
A5: =A30.558=0
A6: =A40.558=0Again, A6 returns TRUE. But A5 returns FALSE because A3 is actually 0.558000000001000. (Again, the binary representation of that constant.)
Note: Ostensibly, "Precision as displayed" rounds to the "precision required" based on cell format. But PAD is fraught with too many problems to be useful, in general.

JoeU commented
I disagree with the suggestion. Generally, calculations should be rounded to the precision required, not to some arbitrary precision. Rounding to 12 decimal places does not hide rounding errors, in general. Two counterexamples....
Example #1:
A1: 34639.969
A2: 5.273
A3: =ROUND(A1A2,12)
A4: =ROUND(A1A2,3)
A5: =A334634.696=0
A6: =A434634.696=0A6 returns TRUE. But A5 returns FALSE because A3 is actually 34634.6959999999. (That is, the binary representaton of that constant.)
Example #2:
A1: 8234.558
A2: 8234
A3: =ROUND(A1A2,12)
A4: =ROUND(A1A2,3)
A5: =A30.558=0
A6: =A40.558=0Again, A6 returns TRUE. But A5 returns FALSE because A3 is actually 0.558000000001000. (Again, the binary representation of that constant.)
Note: Ostensibly, "Precision as displayed" rounds to the "precision required" based on cell format. But PAD is fraught with too many problems to be useful, in general.

Kenneth Barber commented
I turned my comment below into an actual suggestion:
https://excel.uservoice.com/forums/304921excelforwindowsdesktopapplication/suggestions/13341213trackrealandcomplexnumbersasmathematicalexp 
Kenneth Barber commented
You duplicated your own post (your only post for that matter)...
https://excel.uservoice.com/forums/304921excelforwindowsdesktopapplication/suggestions/10705068doweneed15decimalplacesWe should distinguish between the digits shown and the digits used in calculation. You can easily change the number of digits shown using Number formatting.
You have to be careful with your automatic rounding idea. Obviously, it's a good idea if the high precision gives you 5.000...0001 when the answer should be 5.
However, it's terrible for "repeating decimal" or irrational numbers. Take 1/3 * 3 for example. 1/3 doesn't have a precise binary or decimal representation, so we need to represent it as 0.333...333, where the number of 3s is finite. The fewer 3s there are, the less accurate our 1/3 * 3 calculation is. Because of this, having more decimal places is better.
A better suggestion would be for Excel to track mathematical expressions rather than the results of calculations. That way, numbers like 1/3 are represented as 1/3 rather than 0.333.333. Then Excel can simplify expressions like 1/3 * 3 to 3/3 to 1, similar to how we would perform the calculation by hand.
Expression tracking does have its disadvantages, though, such as requiring more memory and slowing down calculations. In other words, it's only good for small spreadsheets.

Bernard Liengme commented
The IEEE roundoff error is forever raising its ugly head. Here is a suggestion.
Nobody needs 15 decimal places. Not even scientists  very few physical constants are known to better than 10 sig figs.
So give us an option (similar to precision as displayed) that automatically round all values to 12 decimal places. 
Kenneth Barber commented
Who needs 15 decimal places? This person:
https://excel.uservoice.com/forums/304921excelforwindowsdesktopapplication/suggestions/10711551morethan15charsinnumbers