For example 5 parts per million means 5/1,000,000.
Percent is a fraction with denominator 100.
For example, 5 percent is 5/100.
So your goal is to convert a fraction with denominator 1,000,000 into a fraction with denominator 100.
Let's work an example:
5 parts per million means 5/1,000,000.
The rules of fractions allow us to multiply the numerator and denominator by the same number (except 0).
So multiply numerator and denominator by .0001 and we get
.0005/100.
Another word for .0005/100 is .0005 percent.
So the general rule is multiply the parts per million by .0001 or divide by 10,000 (same thing).