# SI Unit (Metric) Prefixes

The sizes of the base units are not always convenient for all measurements. For example, a meter is a rather large unit for describing the width of something as narrow as human hair. Instead of reporting the diameter of hair as 0.00012 m, SI also provides a series of prefixes that can be attached to the units, creating units that are larger or smaller by powers of 10. The prefixes are listed in the following table:
 Prefix Abbreviation Factor Example with base unit meters (m) kilo- k 1,000 × 1 km = 1,000 m deci- d 1/10 × (or 0.1 ×) 1 dm = 0.1 m centi- c 1/100 × (or 0.01 ×) 1 cm = 0.01 m milli- m 1/1,000 × (or 0.001 ×) 1 mm = 0.001 m micro- μ* 1/1,000,000 × or (0.000001 ×) 1 μm = 0.000001 m nano- n 1/1,000,000,000 × or (0.000000001 ×) 1 nm = 0.000000001 m *The letter μ is a Greek letter called “mu,” which is pronounced “myoo.”
Some prefixes create a multiple of the original unit: 1 kilogram equals 1,000 grams. Other prefixes create a fraction of the original unit. Thus, 1 centimeter equals 1/100 of a meter, 1 millimeter equals 1/1,000 of a meter, and so forth.
Both SI units and prefixes have abbreviations, and the combination of a prefix abbreviation with a base unit abbreviation gives the abbreviation for the modified unit. For example, kg is the abbreviation for kilogram. We will be using these abbreviations throughout this book.

When you read a measurement in the SI system, it is fairly easy to translate the measurement into a number of the basic units. For example, 5 kg (five kilograms) is the same as 5 × 1000 (the meaning of kilo) grams or 5000 grams. Or 2 mL (two millilitres) is the same as 2 × 0.001 (the meaning of milli) litres or 0.002 litres. This process is discussed further with examples for length, mass, and volume units below.

# Applying Prefixes to Length Units

The SI unit for length is the meter (m). However, just like we use miles or inches instead of feet in the English system, we sometimes need to modify the meter when measuring certain distances. One meter (m) is about 39.37 inches or 1.094 yards. Longer distances, such as distances between cities, are often reported in kilometers (km). There are 1000 m in 1 km:

1 km = 1000 m

Shorter distances, such as the diameter of a cooking pan, can be reported in centimeters (1 cm = 0.01 m). There are 100 cm in 1 m. Another way to say this is that 1 cm is equal to one hundredth of a meter (1/100 m):

1 cm = 1/100 m = 0.01 m

Even shorter distances, like the thickness of a slice of potato, can be measured in millimeters (1 mm = 0.001 m). There are 1000 mm in 1 m. This can also be represented as 1 mm is equal to one thousandth of a meter (1/1000 m):

1 mm = 1/1000 m = 0.001 m

## Example: Understanding the kilo- Prefix

The distance from Gresham to Portland is 27,000 meters (m). What is this distance in kilometers (km)?

#### Solution

We know that 1 km is equal to 1,000 meters. If the distance is 27,000 meters, this is the same as 27 × 1,000 m. If we replace 1,000 m with 1 km, we could also say the distance is 27 × 1 km = 27 km.

# Applying Prefixes to Mass Units

Perhaps you have already noticed that the base unit kilogram is a combination of a prefix, kilo- meaning 1,000 ×, and a unit of mass, the gram. We can apply the kilo- prefix to grams in the same way it was applied to meters above:

1 km = 1,000 m

1 kg = 1,000 g

Thus, there are 1,000 grams (g) in 1 kilogram (kg).

The ingredients are listed in g or kg in many recipes from countries outside the U.S. (especially baking recipes). Since 1 kg is a fairly large quantity of food (1 kg is equal to 2.2 pounds), you will most often see recipes listing ingredients in units of g.

# Applying Prefixes to Volume Units

Two common volume SI units seen in recipes are the liter (L) and the milliliter (mL) (particularly recipes from outside the U.S.). A liter is a little larger than 1 US quart in volume. We can apply the milli- prefix to liters in the same way it was applied to meters above:

1 mm = 1/1000 m = 0.001 m

1 mL = 1/1000 L = 0.001 L

Thus, 1 mL is equal to one thousandth of a L (1/1000 L). Another way to relate these units to each other that may be easier to remember is there are 1,000 mL in 1 L.

You do see L and mL on the labels of some food and drink items in the U.S., for example, a standard bottle of wine has a volume of 750 mL.

## Example: Identifying Prefixes and SI Base Units

Use the table above to give the abbreviation for each unit and define the abbreviation in terms of the base unit.

1. kiloliter
2. microsecond
3. decimeter
4. nanogram

#### Solution

1. The abbreviation for a kiloliter is kL. Because kilo means “1,000 ×,” 1 kL equals 1,000 L.
2. The abbreviation for microsecond is µs. Micro implies 1/1,000,000th of a unit, or “0.000001 ×”, so 1 µs equals 0.000001 s.
3. The abbreviation for decimeter is dm. Deci means 1/10th, or “0.1 ×”, so 1 dm equals 0.1 m.
4. The abbreviation for nanogram is ng. Nano means 1/1,000,000,000th, or “0.000000001 ×”, and equals 0.000000001 g. 