Lesson Objectives

- Demonstrate an understanding of multiplication by powers of 10
- Demonstrate an understanding of division by powers of 10
- Learn how to build a metric conversion prefix chart
- Learn how to convert between metric units of measurement

## How to Convert between Metric Units of Measurement

In our last lesson, we learned how to convert between U.S. customary units of measurement. In this lesson, we will learn how to convert between metric units of measurement. Most people in the U.S. are not familiar with the metric system. This can make metric conversion a bit challenging at first. Once the terminology is learned, the process becomes a bit simpler.

In our table above, we can see the basic units for the metric system. These units are:

We can place a prefix in front of the basic unit to scale up or down:

6000. » 6. » 6

This tells us 6000 grams is equal to 6 kilograms.

Example 1: Change 47 centimeters to hectometers

Let's look at our metric prefix chart: We can see that moving from centi to hecto on our prefix chart gives us a movement of 4 units left. We will match this movement with our number:

47. » 0.0047

47 centimeters = 0.0047 hectometers

Example 2: Change 3.905 dekaliters to deciliters

Let's look at our metric prefix chart: We can see that moving from deka to deci on our prefix chart gives us a movement of 2 units right. We will match this movement with our number:

3.905 » 390.5

3.905 dekaliters = 390.5 deciliters

Example 3: Change 0.591 kilograms to centigrams

Let's look at our metric prefix chart: We can see that moving from kilo to centi on our prefix chart gives us a movement of 5 units right. We will match this movement with our number:

0.591 » 59,100

0.591 kilograms = 59,100 centigrams

Metric System Basic Units | ||
---|---|---|

Weight (Mass) | Volume | Length |

gram | liter | meter |

- meter - used for length
- gram - used for weight (mass)
- liter - used for volume

Metric Prefixes | ||
---|---|---|

Prefix | Meaning | |

kilo | 1000 | |

hecto | 100 | |

deka | 10 | |

basic unit | 1 | |

deci | 1/10 or 0.1 | |

centi | 1/100 or 0.01 | |

milli | 1/1000 or 0.001 |

- 1 kilometer = 1000 meters
- 1 dekagram = 10 grams
- 1 centiliter = 0.01 liters
- 4 hectograms = 400 grams
- hecto means 100, 4 hectograms tells us we have 4 x 100 or 400 grams

- 9 centimeters = 0.09 meters
- centi means 0.01, 9 centimeters tells us we have 9 x 0.01 or 0.09 meters

6000. » 6. » 6

This tells us 6000 grams is equal to 6 kilograms.

### Metric Prefix Chart

We can use a prefix chart to make metric conversion very simple. When we change between metric units, we are essentially just multiplying or dividing by the appropriate power of 10. Each time we move right on the prefix chart we are dividing by 10 and each time we move left we are multiplying by 10. The prefix chart allows us to match the movement on the chart with the movement of the decimal point in the number. Let's look at a sample prefix chart: Typically we use "King Henry Died Unexpectedly Drinking Chocolate Milk" to remember the prefix chart:- King » kilo
- Henry » hecto
- Died » deka
- Unexpectedly » unit (gram, meter, liter)
- Drinking » deci
- Chocolate » centi
- Milk » milli

Example 1: Change 47 centimeters to hectometers

Let's look at our metric prefix chart: We can see that moving from centi to hecto on our prefix chart gives us a movement of 4 units left. We will match this movement with our number:

47. » 0.0047

47 centimeters = 0.0047 hectometers

Example 2: Change 3.905 dekaliters to deciliters

Let's look at our metric prefix chart: We can see that moving from deka to deci on our prefix chart gives us a movement of 2 units right. We will match this movement with our number:

3.905 » 390.5

3.905 dekaliters = 390.5 deciliters

Example 3: Change 0.591 kilograms to centigrams

Let's look at our metric prefix chart: We can see that moving from kilo to centi on our prefix chart gives us a movement of 5 units right. We will match this movement with our number:

0.591 » 59,100

0.591 kilograms = 59,100 centigrams

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