Elementary Topics IIUnit Conversions & Metric Units

Units conversions swap between different units, such as feet to inches.

Example:How many inches are in 3 feet?

We know that there are 12 inches in a foot … or 1 foot = 12 inches

So, 3x12 = 36 inches

What are Unit Conversions?

The metric system is an international decimalized system of measurement.

However, in the U.S., we used what is called the standard units.

What are metric units?

What’s the Difference between Metric and Standard Units?

Measurement Standard Unit Metric Unit

Length/Width Yards, feet, inches Meter, centimeter, millimeter

Mass Pounds Gram, milligram, kilogram, metric ton

Temperature Fahrenheit Celsius

Area Square feet, square yards

Square meters, square centimeters

Volume Cubic feet Liter, cubic centimeter

Speed Miles per hour Meter per secondKilometer per hour

Where are Metric Units Used?

The metric system was first proposed in France by Gabriel Mouton in 1670.

However, it was not until the French Revolution in 1790 where the French Academy of Sciences decided on a common system (at the time, there were 13 distinct measures for a foot)!

A meter is a base unit for 1/10,000,000 of the distance from the equator to the North Pole on a meridian through Paris.

History of the Meter

How many centimeters are in 4 inches? 3 cubic feet is how many cubic inches? 5 yards is how many feet? Which is bigger: a kilometer or millimeter? 3 liters is how many quarts? 1,000 cubic centimeters is equivalent to

how many liters?

Problems you should be able to complete following this lesson:

Length Conversions 1 foot = 12 inches 3 feet = 1 yard

Example: How many yards are in 60 inches?

Basic Length Conversions

Basics of ConvertingRecall the problem we just did…how many yards are in 60 inches?

This is your initial amount

Overall, we want to convert from inches to yards. The first step is to convert

from inches to feet.

Notice that the inches are DIAGONAL from

each otherThis is key to converting.

Our units must cancel.

Now in order to go from inches to

feet, you have to put an EQUAL

conversion about it. So

12 inches = 1 foot

Now in order to go from feet to yards, you have to put an EQUAL conversion

about it. So 3 feet = 1 yard

Notice that feet are DIAGONAL from

each other

Now that we have units that

are in yards (what we

wanted), you simply multiple straight across

the fractions and reduce.

And…you’re done!

1 inch = 2.54 centimeters 1 meter = 39.4 inches 1 foot = 30.48 centimeters 1 kilometer = .621 miles

Example: How many centimeters are in 10 inches?

Standard to Metric Length Conversions

1 minute = 60 seconds 1 hour = 60 minutes 1 day = 24 hours 1 month = 28-31 days (watch for leap years!)

1 year = 12 months

Example: How many seconds are there in 5 days?

Basic Time Conversions

1 dozen = 12 units 12 dozen = 1 gross

Example: Suppose we have 36 eggs. How many gross

is this?

Dozen & Gross

3 teaspoons (tsp) = 1 tablespoon (tbsp) 2 tablespoons = 1 ounce (oz) 8 oz = 1 cup 2 cups = 1 pint (pt) 2 pints = 1 quart 4 quarts = 1 gallon 31.5 gallons = 1 barrel

Example: Suppose you have 5 quarts of iced tea. How

many cups can you serve?

Basic Measurements

Example: 10 oz equals how many teaspoons?

Example: 400 pints equals how many gallons?

Basic Measurements Continued

Fahrenheit and Celsius

Example: If it is 80°F, what is the temperature in

Celsius?

If it is 32°C, what is the temperature in Fahrenheit?

Temperature Conversions

1 Kg = 2.2 lbs 1 liter = 1000 cm3

1 liter = 1.06 qt 1 gal = 3.8 liters 1 ton = 2,000 lbs (short) or 2,240 lbs (long)

Example: How many cubic centimeters (cm3) are in 2

liters?

Volume/Weight Conversions

deci: 1/10 = 10-1 deca: 10 = 101

centi: 1/100 = 10-2 hecto: 100 = 102

milli: 1/1,000 = 10-3 kilo: 1,000 = 103

micro: 1/1000000 = 10-6 mega: 1,000,000 = 106

nano: 10-9 giga: 109

Example: 100 millimeters (mm) is how many centimeters (cm)?

Prefixes

Example: What is bigger: 100 millimeters or 1

kilometer?

Prefixes Continued

Base

1 kilometer!

When we are dealing with units that are squared (such as when finding area) or cubed (such as when finding volume), we have to be careful with our units! Let’s take a look.

Example: A cube’s volume is 1,000 cubic centimeters

(cm3). What is its volume in inches?

Squared and Cubic Unit Conversions

or

So, I’ve attached a conversion sheet with all of these conversions listed on for you to reference.

But, take a look at a few problems and see how you do. I’ll post an answer key either later in the week, or we can go over any questions during our next class.

You’re almost done…