Unit conversions are important in all sciences, although they may seem more critical in chemistry because many calculations use different units. Every measurement you take should reporting with the proper units. While it may take practice to master unit conversions, you only need to know how to multiply, divide, add, and subtract to do them. The math is easy as long as you know which units can be converted from one to another and how to set up conversion factors in an equation.

### Know the Base Units

There are several common base quantities, such as mass, temperature, and volume. You can convert between different units of a base quantity, but may not be able to convert from one type of quantity to another. For example, you can convert grams to moles or kilograms, but you can't convert grams to Kelvin. Grams, moles, and kilograms are all units that describe the amount of matter, while Kelvin describes temperature.

There are seven fundamental base units in the SI or metric system, plus there are other units that are considered base units in other systems. A base unit is a single unit. Here are some common ones:

Mass | kilogram (kg), gram (g), pound (lb) |

Distance or Length | meter (m), centimeter (cm), inch (in), kilometer (km), mile (mi) |

Time | second (s), minute (min), hour (hr), day, year |

Temperature | Kelvin (K), Celsius (°C), Fahrenheit (°F) |

Quantity | mole (mol) |

Electric Current | ampere (amp) |

Luminous Intensity | candela |

### Understand Derived Units

Derived units (sometimes called special units) combine the base units. An example of a derived unit is a unit for area, square meters (m^{2}) or the unit of force, the newton (kg·m/s^{2}). Also included are volume units. For example, there are liters (l), milliliters (ml), cubic centimeter (cm^{3}).

### Unit Prefixes

In order to convert between units, you'll want to know common unit prefixes. These are used primarily in the metric system as a sort of shorthand notation to make numbers easier to express. Here are some useful prefixes to know:

Name | Symbol | Factor |

giga- | G | 10^{9} |

mega- | M | 10^{6} |

kilo- | k | 10^{3} |

hecto- | h | 10^{2} |

deca- | da | 10^{1} |

base unit | -- | 10^{0} |

deci- | d | 10^{-1} |

centi- | c | 10^{-2} |

milli- | m | 10^{-3} |

micro- | μ | 10^{-6} |

nano- | n | 10^{-9} |

pico- | p | 10^{-12} |

femto- | f | 10^{-15} |

As example of how to use the prefixes:

1000 meters = 1 kilometer = 1 km

For very large or very small numbers, it's easier to use scientific notation:

1000 = 10^{3}

0.00005 = 5 x 10^{-4}

### Performing Unit Conversions

With all of this in mind, you're ready to perform unit conversions. A unit conversion can be thought of as a sort of equation. In math, you may recall if you multiply any number times 1, it is unchanged. Unit conversions work the same way, except "1" is expressed in the form of a conversion factor or ratio.

Consider the unit conversion:

1 g = 1000 mg

This could be written as:

1g / 1000 mg = 1 or 1000 mg / 1 g = 1

If you multiply a value times either of these fractions, its value will be unchanged. You'll use this to cancel out units to convert them. Here's an example (notice how the grams cancel out in the numerator and denominator):

4.2x10^{-31}g x 1000mg/1g = 4.2x10^{-31} x 1000 mg = 4.2x10^{-28} mg

### Using Your Calculator

You can enter in these values in scientific notation on your calculator using the EE button:

4.2 EE -31 x 1 EE3

which will give you:

4.2 E -18

Here's another example. Convert 48.3 inches into feet.

Either you know the conversion factor between inches and feet or you can look it up:

12 inches = 1 foot or 12 in = 1 ft

Now, you set up the conversion so that the inches will cancel out, leaving you with feet in your final answer:

48.3 inches x 1 foot/12 inches = 4.03 ft

There is "inches" in both the top (numerator) and bottom (denominator) of the expression, so it cancels out.

If you had tried to write:

48.3 inches x 12 inches/1 foot

you would have had square inches / foot, which wouldn't have given you the desired units. Always check your conversion factor to make sure the correct term cancels out!

You may need to switch the fraction around.

### Key Points

- Unit conversions only work if the units are the same type. For example, you can't convert mass into temperature or volume into energy.
- In chemistry, it would be nice if you only had to convert between metric units, but there are many common units in other systems. For example, you may need to convert a Fahrenheit temperature into Celsius or a pound mass into kilograms.
- The only math skills you need to do unit conversions are addition, subtraction, multiplication, and division.