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So I have the a formula that outputs a duration as seconds with three digits of milliseconds.

For example if the formula outputs 67.769, It should be formatted as 01:07.769

I tried using mm":"ss"."000, but that gave me 27:21.600

It seems to be trying to process the number as a date; how do I prevent this?

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The date-time value unit in Google Sheets is one day, so you should convert your formula output to days, then apply the duration formatting.

Assume that the referred formula is on cell A1 and that you want to get the result on cell B1. The formula to use on B1 one could be

=A1/60/24

or something similar.

Then apply to B1 the following custom format [h]:mm:ss.000

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