Step-by-step explanation:
a whole number has 0 decimal places (after the decimal point, meaning on the right side of the decimal point).
so, all the decimal places (4) must come from the other factor.
a multiplication by a whole number is always a series of additions of the other factor with itself. if anything, such a multiplication eliminates decimal places. it does not create additional ones.
e.g.
3.06 × 5 = 15.3 (because it is actually 15.30, but trailing 0s don't have any value like leading 0s, and are normally skipped).
the increase in the decimal places happens by involving places with higher value : 1/10 has a higher value than 1/100, that has a higher value than 1/1000, and so on.
so, e.g. 0.2×9 = 1.8 (and not 0.18).
as it is 2/10 × 9 = 18/10 = 1.8
an addition cannot create suddenly new decimal places with lower value.
therefore, normally we would say the other factor has 4 decimal places.
but in reality, it is a I said above, the 4 decimal places of the result of the multiplication "come from the other factor".
we cannot say that the other factor has 4 decimal places, because it could have more, and the multiplication with the whole number removed some.
e.g. 3.6 × 5 = 18 (or 18.0).
so,
32.3046 could be 6.46092 × 5
when we think this through, the other factor could have infinitely many decimal places.
like 5/9 × 108 = 0.555555... × 108 = 60
or our number
32.3046 could be 0.2991166666... × 108
so, all we can say, the other factor must have at least 4 decimal places.