is number between values
 

I am measuring a selection of cast metal parts. What formula do I use to
determine whether the dimension is highrer than the upper limit or lower than
the lower limit.
The high limit is .7129", the low limit is .5943"

is number between values
 

Presuming value to work with is in A1, use this formula:

=IF(A10.7129,"HIGH",IF(A1<0.5943,"LOW",A1))


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is number between values
 

Lotus123 wrote...
Presuming value to work with is in A1, use this formula:

=IF(A10.7129,"HIGH",IF(A1<0.5943,"LOW",A1))
....

More condensed than the other responses, but why not use a table
lookup?

=LOOKUP(A1,{0;0.5943;0.7129},{"LOW";"OK";"HIGH"})

Note that in the wonderful world of Excel, if A1 contained text or
boolean (TRUE/FALSE) values, the IF formula would invariably return
HIGH since text and both boolean values are treated as greater than any
number value, but the LOOKUP formula returns #N/A when A1 is text or
boolean.