What is the best way to split a string into integers and units?
We can use APPLY to calculate the position of the various things we need, we use each APPLY in series like variables in procedural code.
We assume that the number is the start of the string, followed by arbitrary letters, a slash, another number, then more letters.
Note: no tally function needed here:
            
select
    cost,
    size,
    strength,
    v4.*

from example e

cross apply ( values (
    charindex('/', e.strength)
) ) as v1 (slash)

cross apply ( values (
    iif(slash = 0, e.strength, left(e.strength, slash - 1)),
    substring(e.strength, nullif(slash, 0) + 1, len(e.strength)) -- len means the rest of string
) ) as v2 (numer, denumer)

cross apply ( values (
    patindex('%[^0-9.]%', numer),  -- first non-number
    patindex('%[^0-9.]%', denumer)
) ) as v3 (numerUnit, denumerUnit)

cross apply ( values (
    try_cast(iif(numerUnit = 0, numer, left(numer, numerUnit - 1)) as real),
    iif(numerUnit = 0, null, substring(numer, numerUnit, len(numer))),

    try_cast(iif(denumerUnit = 0, denumer, left(denumer, denumerUnit - 1)) as real),
    iif(denumerUnit = 0, null, substring(denumer, denumerUnit, len(denumer)))
) ) as v4 (numerator, numeratorUnit, denumerator, denumeratorUnit)