In the Map Calculator use an expression like
[My grid . Count].Float
"My grid" is the name of an integer grid and "Count" is the name of a field in its attribute table. A single space on each side of the "." is essential. It's best not to type this yourself: you can find a list of all such grid+field combinations displayed within the Map Calculator dialog. Double-click on the one you want. This copies its name into the input textbox. Then type the ".Float" part directly.
You can create extended Map Calculator expressions if you like, as in
[My grid . Count].Float / 100.0
Be careful, though: the syntax is not entirely documented; it is strange; and it is finicky. (It seems nothing has really changed over the last 20 years except for the details. :-) For example, "100." will not work; you need to write "100.0". As another example, if you fail to include ".Float", ArcView will perform integer arithmetic, even though "100.0" is explicitly floating point. Therefore, it's usually best to do just one thing in each Map Calculator expression, checking the results carefully after each step. To make it possible to reproduce your work later, I recommend copying and pasting the MC expressions either into a Script Editor document or into the "comments" field of the grid theme's "Theme Properties" dialog as you go along. Save your work early and often, too... .
For a complete list of things you can do with grids in the Map Calculator, see the help page for "Grid (class)".