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how is the conversion factor used for converting derived units?

See below  

Step-by-step explanation:

A derived unit is a unit that is derived from the SI base units. Examples are cm, m² and kg/m³.

Conversion factors are ratios of units that are equal to one.  

Thus. you can multiply any measurement by a conversion factor to get its value in other units.

Here's a question that uses conversion factors:

How many centimeters are in 3.4m?

You know that "centi" means "× 10⁻²", so

1 cm = 10⁻² m

If you divide both sides by 1 cm, you get the ratio: 1 = 10⁻² m/1 cm.

If you divide both sides by 10⁻² m, you get the ratio: 1 cm/10⁻² m = 1.

Thus,

10⁻² m/1 cm = 1 cm/10⁻² m = 1

Both ratios are conversion factors because they both equal one and multiplying a measurement by one does not change its value.

You choose the conversion factor that gives you the correct dimensions for your answer. It must have the correct dimensions on top (in the numerator),

Thus, to convert 3.4 m to cm, you use the conversion factor with “cm” on  top.

∴ Length = 3.4 m × (1 cm/10⁻²m ) = 340 cm

Notice that the unwanted units of "m" also cancel during the operation.

If you had used the other conversion factor, you would have gotten

Length = 3.4 m × (10⁻²m/1 cm) = 0.034 m²/cm

The units of the answer don't make sense, so you know you have used the wrong conversion factor.

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