mjhjmtu

Use xfp:

7.0pt

documentclassarticle

usepackagexfp

begindocument

newlengthmyLength%
setlengthmyLengthfpevalround(0.7 * topskip, 0)pt%
themyLength

enddocument

Dimensions in fpeval are converted to pt and stripped of the dimension part in order to perform calculations (hence the addition of a "closing pt").

If you want you can define

newcommandmult[2]fpevalround(#1 * #2, 0)pt

to support your input

setlengthmyLengthmult0.7topskip

There is no way to get a length of 458752sp from <factor>topskip if topskip has the value 10pt, that is, 655360sp, because TeX don't do floating-point computations, but fixed-point base two arithmetic.¹

The binary representation of 7/10 is 0.10(1100), parentheses denote the period. and the multiplication rules of TeX can only provide either 458750sp or 458760sp, represented respectively as 6.99997pt and 7.00012pt.

The difference between the upper and lower best representations is 10sp, which is less than 0.000435 millimeters or 0.00016 points.

Since the usual value of vfuzz is 0.1pt (less than 0.03mm), there should be no concern about getting an “exact” value: you'd need to cumulate more than 680 such errors in order to exceed the vfuzz.

documentclassarticle

newlengthmultipletopskip

begindocument

Topskip: thetopskip (numbertopskip sp)

70% topskip: thedimexpr 7topskip/10relax (numberdimexpr 7topskip/10relax sp)

setlengthmultipletopskip0.7topskip
0.7 topskip: themultipletopskip (numbermultipletopskip sp)

setlengthmultipletopskip0.70001topskip
0.70001 topskip: themultipletopskip (numbermultipletopskip sp)

enddocument

As you see, 0.7topskip is accurate up to 2sp, less than 0.00009mm.²

Unless you completely override TeX's computation by using a different model such as IEEE754 (decimal32) as is done in Werner's answer, you can't get “exact” values.

Footnotes

¹ When TeX was written, there was no agreed upon standard for floating-point computations and Knuth's aim was to obtain the same output on every machine TeX was implemented on. Using 64 bits instead of 32 could have achieved “better” accuracy, but at the expense of speed and need for memory: PC's of that time might have even less than 640 kiB of RAM.

² Being a skip, it would be more sensible to use glueexpr rather than dimexpr, as noted by GuM in comments. Note that <factor><skip register> will discard the plus and minus components, whereas multiply and divide don't. So

setlengthmultipletopskipglueexprtopskip*7/10relax

could be better.

This should not be an answer, but rather a comment both to @egreg’s answer and to David Carlisle’s; unfortunately, I need to include some sample code, and this can only be done (in an intelligible form) in an answer. I willingly concede that it doesn’t add anything substantial to those two answers—except, perhaps, a bit of clarity. I’m ready to remove this answer if either of the abovementioned authors clarifies his.

As already repeatedly remarked, Knuth’s TeX does (or rather, did) its calculations with dimensions using 32-bit fixed points arithmetics; all modern typesetting engines, however, incorporate the so-called “e-TeX” (for Extended, or Enhanced, TeX) extensions, among which is the ability to perform dimension scaling, that is, multiplication of a dimension for a fraction, with 64-bit precision. More precisely, e-TeX extensions introduce a new type of syntax by means of which dimensions can be specified, that enables the use of “expressions”, in the customary sense of the term; in particular, you are allowed to multiply a certain dimension for a fraction, as in

setlengthsomeotherdimendimexpr somedimen * 7/10

(the primitive dimexpr marks the beginning of a “dimen-valued” expression; the end is implicitly marked by the first token that cannot be interpreted as part of the expression itself—you can assume it is the closing brace, in the above example). When this is done, a 64-bit temporary register is used to hold the intermediate result of the multiplication of the dimension for the numerator of the fraction (somedimen * 7, in the above example); thank to this expedient, when the subsequent division for the denominator (10, in our case) is performed, all bits of the final (32-bit) result are significant.

As already said, dimexpr starts a “dimen-valued” expression; there exists a similar primitive for “glue-valued” expressions, named glueexpr. Note, however, the difference, that others have already explained, between

setlengthsomeotherskipglueexpr 7someskip /10

and

setlengthsomeotherskipglueexpr someskip * 7/10

In the former, 7someskip is converted to a dimen value, destroying (that is, zeroing) its stretch and shrink components, if any; this doesn’t happen with the latter.

The following code proves that

setlengthsomeotherskipglueexpr topskip * 7/10

attains the same precision as explicitly setting someotherskip to 7pt (and similarly for the stretch and shrink components, if present):

% My standard header for TeX.SX answers:
documentclass[a4paper]article % To avoid confusion, let us explicitly 
 % declare the paper format.

usepackage[T1]fontenc % Not always necessary, but recommended.
% End of standard header. What follows pertains to the problem at hand.

newcommand*ReportDimen[2]%
 #1:>textttthe #2\>texttt(number #2sp)\%

newcommand*ReportGlue[2]%
 #1:>textttthe #2\>%
 texttt(%
 number #2sp
 plus numberexpandafterdimexprthegluestretch #2relax sp
 minus numberexpandafterdimexprtheglueshrink #2relax sp%
 )\%


setlengthtopskip10.0pt plus 1pt minus 1 pt
newlengthsmallertopskip
 setlengthsmallertopskip.700004577636718749999999999999999999999999999999topskip
newlengthlargertopskip
 setlengthlargertopskip.700004577636718750000000000000000000000000000000topskip
newlengtheTeXTopskip
 setlengtheTeXTopskipglueexpr topskip * 7/10
newlengthsevenpoints
 setlengthsevenpoints7.0pt plus .7pt minus .7pt



begindocument

begintabbing
 Topskip:quad=kill
 ReportGlue Topskiptopskip
 ReportDimenSmallersmallertopskip
 ReportDimenLargerlargertopskip
 ReportGlue eTeX'seTeXTopskip
 ReportGlue Exactsevenpoints
endtabbing

enddocument

(values in scaled points are shown as well).