How I can convert the value of a unit into an other unit?

Question

I have to convert a value from the old unit into the new unit.

The old unit can be mg/l and the new unit can be ug/ml. The oldValue is 8 mg/l. When I use the converter of google it shows me that the value doesn't change. In my calculation the value changes from 8mg/l to 1 ug/ml, what is absolutely wrong.

Most probably I am using the incorrect formula to calculate the new value.

This is my current approach:

At first, I declared the possible units with objects and the potencies:

  private potenciesMass = {
    kg: 1,
    g: 1000,
    mg: 1000000,
    µg: 1000000000,
    ug: 1000000000,
    pg: 1000000000000,
  };

  private potenciesCapacity = {
    l: 1,
    dl: 10,
    ml: 1000,
    ul: 1000000,
    nl: 1000000000,
    pl: 1000000000000,
    fl: 1000000000000000,
  };

In the next step I read out the potency of each unit and calculate the new value with them. At the end I divide both values.

 let potencyFirstOld = this.getPotencyValue(oldUnitSplitted[0]);
        let potencyFirstNew = this.getPotencyValue(newUnitSplitted[0]);

        // Second Unit
        let potenceySecondOld = this.getPotencyValue(oldUnitSplitted[1]);
        let potenceySecondNew = this.getPotencyValue(newUnitSplitted[1]);

        let firstValue = this.convertMultipleTypes(
          potencyFirstOld,
          potencyFirstNew,
          value
        );

        let secondValue = this.convertMultipleTypes(
          potenceySecondOld,
          potenceySecondNew,
          value
        );

        value = firstValue / secondValue;

Anyone have an idea how I can convert the old value into the new value by the units?

Edit: New Code

  private convertMultipleTypes(
    potencyOld: number,
    potencyNew: number,
    value: number
  ): number {
    let potenceDifference = 0;
    let potence: number;

    if (potencyOld < potencyNew) {
      potenceDifference =
        potencyNew.toString().length - potencyOld.toString().length;
      potence = this.calculatePotence(potenceDifference);
      return value / potence;
    }

    potenceDifference =
      potencyOld.toString().length - potencyNew.toString().length;
    potence = this.calculatePotence(potenceDifference);
    return value * potence;
  }

  private calculatePotence(potenceDifference: number): number {
    let potence = "1";

    for (let i = 0; i < potenceDifference; i++) {
      potence += 0;
    }

    return Number(potence);
  }