Unit ConversionsRatios and Examples

Meter

s

Centimeters

Ratios

Distance- US 1 inch= 2.54 centimeters 1 foot= 12 inches 1mile= 5280 feet 1 yard= 36 inches 1 mile= 5280 feet 1 yard=3 feet

Ratios

Distance- Metric 1 centimeter= 10 millimeters 1 meter=100 centimeters 1 meter=1000 millimeters 1 kilometer= 1000 meters 1 meter= 39.37 inches 1 meter= 1.06x10^-16 Light years 1 meter= 0.00021 miles 1 meter= 1.0936 yards 1 meter=3.28 feet

Ratios

Volume- US 1 cup= 8 ounces 1 pint= 2 cups 1 quart= 2 pints 1 Gallon= 4 quarts

Ratios

Temperatures 1 Kelvin= -272.15 oC 1 Kelvin= -457.87oF oC= (oF-32)

1.8

Ratios

Time 1 minute= 60 seconds 1 hour= 60 minutes 1 day= 24 hours 1 week= 7 days 1 year= 52 weeks 1 decade= 10 years 1 century= 10 decades

Ratios

Weight/Mass 1 kilogram=1000 grams 1 gram= 1000 milligrams 1 gram= 0.0022 pounds 1 gram= o.o35 ounces 1 gram= 1.102x10^-6 tons 1 pound= 16 ounces 1 ton= 2000 pounds

Ratios

Volume 1 Liter= 0.001 cubic meters 1 Liter= 1000 milliliters 1 Liter= 0.264 gallons 1 Liter= 1.056 quarts 1 Liter= 2.113 pints 1 Liter= 4.227 cups 1 Liter=33.8 fluid ounces 1 Liter= 0.035 cubic feet

Why Use It?

When different units are used, sometimes it makes the numbers easier to manipulate Very large and very small numbers are

easier to work with after they are either made smaller or larger

Some equations call for a specific unit

How do you convert to a different unit?

Start by making a grid like this

Next put the unit that you have in the upper left hand space e.g.

Meters

How do you convert to a different unit?

Next place the unit you want to get to in the far upper right hand space.

Meters Centimeters

How do you convert to a different unit?

Now we need to determine what goes into the middle.

This will be a ratio of the unit you have and the unit you want.

For this example we can use the relationship between meters and centimeters Meters Centimeters Centimeters

Meters

How do you convert to a different unit?

Which unit do you put on top and which unit to put on the bottom?

The unit on bottom much be diagonal to the unit you already have. Meters Centimeters Centimeters

Meters

Using more than one step to get a new unit

Follow the same rules e.g. Kilograms milligrams

Go from Kilograms to grams, then grams to milligrams

Kilograms Grams milligrams milligrams

Kilograms Grams

Now let’s add some numbers

Remember: in ratios the number 1 ALWAYS goes with the larger unit.

2 Meters 100 Centimeters 200 Centimeters

1 Meter

Larger Unit

Unit Conversion Calculations How do you actually calculate how much of

something you have in the new units? Every time you see a vertical line multiply Every time you see a horizontal line divide

2Meters 100 Centimeters 200 Centimeters

1 Meter

2 Meters 100 Centimeters 200 Centimeters

1 Meter

Unit Conversion

We can also go from smaller units to larger units following the same method.

560 mg 1 g 0.56 g 1000mg

Note: The matching units are still diagonal to each other and the 1 goes with the larger unit.

Larger Unit

Units match

Example

Example: How many inches are in one mile?

1 mi 5280ft 12 in 63,360 inches

1mi 1 ft

Example

Example: How many milligrams are there in a 0.56 g sample?

0.56 g 1000 mg 560 mg 1 g

Example

Example: How many days are in 54,320 minutes?

54,320 minutes 1 hour 1 day 37.7 days

60 minutes 24 hours