CountIF date/time not counting correctly

I'm using Index/Match to fill other rows with the dates in order they occur. It intermittently fails and I believe the nested Countif formula isn't working consistently with the date. Column A is formatted "m/d/yyyy h:mm:ss"

The dates start in A1, and B1 formula is =COUNTIF($A$1:$A$6,"<="&A1). I believe this should return the order in the range in which the time occurs.
11/27/2019 15:04:05
11/27/2019 14:49:06
11/27/2019 14:34:06
11/27/2019 14:19:06
11/27/2019 15:14:05

This populates Column B row 3 & 4 with 1, and subsequent formulas dont' work.
If I change row A3 by 1 second the formula works.

Is there a problem with the date/format? I've tried using a serial date and that doesn't work either. I appreciate any advice.

Welcome to the forum

Please attach a sample workbook (not a picture or pasted copy). Make sure there is just enough data to demonstrate your need. Include a BEFORE sheet and an AFTER sheet in the workbook if needed to show the process you're trying to complete or automate. Make sure your desired results are shown, mock them up manually if necessary.

Remember to desensitize the data.

Click on GO ADVANCED and then scroll down to Manage Attachments to open the upload window.

Use SUMPRODUCT instead

=SUMPRODUCT(--($A$1:$A$5<=A1))

Copy down

An attachment was not necessary. The phenomenon is easy to reproduce. Adding to the mystery:

1. If we enter the =A1<=$A$3 into C1 and copy down, C3 and C4 are TRUE, confirming that there should be 2 matches.
2. =COUNTIF($A$1:$A$6,"<=11/27/2019 2:34:06 PM") returns 2.
3. =COUNTIF($A$1:$A$6,"<=11/27/2019 14:34:06") returns 2.
4. Simplification of the problem: =COUNTIF(A3,"<="&A3) returns zero(!).

My guess is: the problem is a binary floating-point anomaly, compounded by the games that Excel plays.

Note that =A3-TEXT(A3,"0.00000000000000E+0")<=0 returns FALSE, but A3<=TEXT(A3,"0.00000000000000E+0") returns TRUE.

In the first formula, Excel compares the exact binary difference.

In the second formula, Excel compares each operand rounded to 15 significant digits.

The exact binary value of 11/27/2019 14:34:06 can be represented by 43796.6070138888 + 8.73E-11, where for A3, Excel displays 43796.6070138888(!) when rounded to 15 significant digits (formatted as Number with 12 decimal places).

(That should round to 43796.6070138889. Off-hand, I cannot explain why it doesn't with impunity. I suspect that it is related to the same formatting defect that causes 42304.973 to be displayed as 42304.9729999999 in the Formula Bar.) (1)

Two work-arounds:

=COUNTIF($A$1:$A$6,"<="&TEXT(A3,"m/d/yyyy h:m:s"))
or
=SUMPRODUCT(($A$1:$A$6<>"")*($A$1:$A$6<=A3))


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(1) I confirmed that the conditions that apply to the defective formatting of 42304.973 also apply to the binary value of 11/27/2019 14:34:06, which can represented by 43796.6070138888 + 8.73E-11, to wit: (a) the integer part is less than 65536 (2^16); (b) the fractional part can be represented in 32 bits or less (i.e. any bits to the right are zero); and the 16th significant digit is 5 or more. In that case, Excel fails to round up the 15th significant digit, as we would expect.