(COP) Metric to Metric Conversions Lesson

Metric to Metric Conversions

The benefit of using the metric system is that it is easy to convert between units. The English system can be very difficult to convert between units because you need to remember the conversions between each unit.  For instance, if you were wanting to find out how many inches were in a mile there are conversions you would need to know to be able to calculate your answer.

English Conversion System

Unit

Converted Unit

12 inches

1 foot

3 feet

1 yard

1760 yards

1 mile

This can be very complicated.  However, converting between kilometers and centimeters can be very simple.

In order to convert from one metric unit to another, it is important to know the order of the metric prefixes.  Many people use mnemonic devices, or sayings, to help them remember the order of things.   It is important to find a mnemonic device that will be easy for you to remember.  A common saying to remember the order from large units to small units is King Henry Died by drinking chocolate milk.  There are many ways in which you can convert between the units.  Let's go over two methods below and you can choose which works best for you.

King-Kilometer-1000 m Henry-Hectometer-100 m Died-Decameter-10 m By-Meter-1 m Drinking- Decimeter-0.1 m Chocolate-Centimeter-0.01 m Milk-Millimeter-0.001 m

Method 1:

  1. Start with the given value
  2. Insert the conversion factors as fractions
  3. Do the math

Example:   How many centimeters are in 5.2 kilometers?

LaTeX: \frac{5.2\hspace{.2cm}kilometers}{1}\hspace{.2cm}x\hspace{.2cm}\frac{1000\hspace{.2cm}meters}{1\hspace{.2cm}kilometer}\hspace{.2cm}x\hspace{.2cm}\frac{100\hspace{.2cm}centimeters}{1\hspace{.2cm}meter} = 520,000\hspace{.2cm}centimeters5.2kilometers1x1000meters1kilometerx100centimeters1meter=520,000centimeters

Method 2:

  1. Write out the order of the prefixes in a stair step from largest unit to smallest unit.
  2. Start at the stair of the unit that is given.
  3. Count the number of steps to the new unit.
  4. Move the original unit's decimal point the same number of places in the direction you go on the stair step (up you move the decimal to left; down you move the decimal to right).
  5. Fill in zeros in order to hold the decimal spot.

Example:   How many kilometers are in 468.75 millimeters?

Step 1:

In a stair step formation Kilo-1000 Hecto-100 Deca-10 Base-1 Deci-.1 Centi-.01 Milli-.001

Step 2:

In a stair step formation Kilo-1000 Hecto-100 Deca-10 Base-1 Deci-.1 Centi-.01 Milli-.001-with a red dot on the bottom stair indicating that's where you start

Step 3:

In a stair step formation Kilo-1000 Hecto-100 Deca-10 Base-1 Deci-.1 Centi-.01 Milli-.001-with red dot starting at the bottom step and then 6 red hairs showing 6 places moved

Step 4:

468.87 with red arrow starting under the decimal "jumping" 6 places to the left

Step 5:

.00046875

Answer:   468.75 millimeters = .00046875 kilometers

The video below will discuss converting within the metric system. 

The video below will show you how to use the metric staircase. 

Examples

  1. 752.6 m =_______km

Solution: Look for a unit factor that contains both meters and kilometers.

1000 m = 1 km

Multiply by the unit factor.  Be sure to put the units you want to change from in the denominator. 

LaTeX: ( 752.6 m = \frac{1 km}{1000 m}= .7526 m)(752.6m=1km1000m=.7526m)

Cross cancel m.

LaTeX: ( 752.6 \cancel{m} = \frac{1 km}{1000 \cancel{m}}= .7526 m)(752.6m=1km1000m=.7526m)

Dividing by 1000 moves the decimal 3 places to the left.

 

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