# 1.9: Developing Conversion Factors

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Learning Objectives
• Represent equalities as conversion factors.

A conversion factor is a fraction in which both the numerator (the part of a fraction that is written above the fraction bar) and the denominator (which is written below the fraction bar) contain numbers and units.  Conversion factors are used to change one unit of measurement into another. A simple conversion factor can be used to convert meters into centimeters, or a more complex one can be used to convert miles per hour into meters per second. Since most calculations require measurements to be expressed in certain units, there are many uses for conversion factors.

Conversion factors are derived from equalities, which were discussed in the previous section.  In Example 1.6.2, the following prefix modifier equality was developed.

$${ \text{100 cm}} = { \text{m}}$$

To create a conversion factor from this equality, write the quantity on one side of the equal sign in the numerator of a fraction, and write the other quantity in the denominator.

$$\dfrac{ \text{100 cm}}{\text{m}}$$

Note that a second conversion factor could be developed by interchanging where each quantity is written, relative to the fraction bar.

$$\dfrac{ \text{m}}{\text{100 cm}}$$

Exercise $$\PageIndex{1}$$

Create two conversion factors from each of the following equalities.

1. $${ \text{kg}} = { \text{1000 g}}$$
2. $${ \text{1 ft}} = { \text{12 in}}$$
3. $${ \text{1 h}} = { \text{60 min}}$$
$$\dfrac{ \text{kg}}{\text{1000 g}}$$ and $$\dfrac{ \text{1000 g}}{\text{kg}}$$
$$\dfrac{ \text{1 ft}}{\text{12 in}}$$ and $$\dfrac{ \text{12 in}}{\text{1 ft}}$$
$$\dfrac{ \text{1 h}}{\text{60 min}}$$ and $$\dfrac{ \text{60 min}}{\text{1 h}}$$