## Chemistry Tutorial

*Converting between Metric Units *

#### Intro

The Metric System is based on the fundamental units of measure for length, volume, and mass.

**Length: meter (m) Volume: liter (L) Mass : gram (g)**

Base units in the Metric System can be converted into units that are more appropriate for the quantity being measured by adding a prefix to the name of the base unit. The common metric prefixes are given below.

**Metric System Prefixes**

Prefix Symbol Meaning

femto- f x 1/1,000,000,000,000,000 (10-15)

pico- p x 1/1,000,000,000,000 (10^-12)

nano- n x 1/1,000,000,000 (10^-9)

micro- u x 1/1,000,000 (10^-6)

milli- m x 1/1,000 (10^-3)

centi- c x 1/100 (10^-2)

deci- d x l/10(10^-1)

kilo- k x 1,000 (10^3)

mega- M x 1,000,000 (10^6)

giga- G x 1,000,000,000 (10^9)

tera- T x 1,000,000,000,000 (10^12)

Prefix Symbol Meaning

femto- f x 1/1,000,000,000,000,000 (10-15)

pico- p x 1/1,000,000,000,000 (10^-12)

nano- n x 1/1,000,000,000 (10^-9)

micro- u x 1/1,000,000 (10^-6)

milli- m x 1/1,000 (10^-3)

centi- c x 1/100 (10^-2)

deci- d x l/10(10^-1)

kilo- k x 1,000 (10^3)

mega- M x 1,000,000 (10^6)

giga- G x 1,000,000,000 (10^9)

tera- T x 1,000,000,000,000 (10^12)

The base units of length and volume are linked in the metric system. By definition, a liter is equal to the volume of a cube exactly 10 cm tall, 10 cm long, and 10 cm wide. Because the volume of this cube is 1000 cubic centimeters and a liter contains 1000 milliliters, 1 milliliter is equivalent to 1 cubic centimeter.

**1 mL = 1cm3**

The base units of volume and weight are also linked. The gram was originally defined as the mass of 1 mL of water at 4 degrees Celsius.

**1g = 1mL H2O at 4 ºC**

#### Sample Problem

Convert 0.279 kilometers to meters

#### Solution

In order to convert 0.279 kilometers to meters, you must understand how many meters are in 1 kilometer.

There are 1000 meters in 1 kilometer, which you can write like this:

**1000 meters = 1 kilometer**

From there you must understand which unit is the “larger” unit. Since 100 meters could fit inside 1 kilometer, the kilometer is the larger unit. Just as if 1000 cherries could fit inside one basket, the basket is the larger item. So use multiplication to understand how many meters are in the kilometer measurement.

Simply:

**1000 meters = 1 kilometer**

x meters = 0.279 kilometers

x meters = 0.279 * 1000 meters

x meters = 279 meters

# About The Author

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I am a Master's degree graduate from the University of Connecticut focusing in Biological Oceanography, and estuarine processes. My tutoring experience began way back as a volunteer peer tutor in my high school library. Since then, I have 2 years experience tutoring as a paid peer tutor during my un... |