Introduction
If you go to a grocery store in the United States, milk is usually sold in one gallon containers. Another way to measure the same volume of milk is using Liters. Each one gallon container is approximately equal to 3.75 Liters.
Gallons and Liters are different units of measurement that we can use to quantify volume.
We use many different units of measurement to quantify the same items.
Distance is the measure of how far apart things are.
Here are some common distance conversions we use every day:
Distance Conversions
1 kilometer (km) is equal to 1000 meters (m)
1 km = 1000 m
1 meter (m) is equal to 100 centimeters (cm)
1 m = 100 cm
1 mile (mi) is equal to 5280 feet (ft)
1 mi = 5280 ft
1 foot (ft) is equal to 12 inches (in)
1 ft = 12 in
1 yard (yd) is equal to 3 feet (ft)
1 yd = 3 ft
1 meter (m) is approximately equal to 3.3 feet (ft)
1 m ≈ 3.3 ft
Volume is a measure of the interior space of a 3D object. A cube, cylinder, milk jug or any 3D shape will have volume inside of it.
Here are some common volume conversions we use every day:
Volume Conversions
1 Liter (L) is equal to 1000 milliliters (ml)
1 L = 1000 ml
1 gallon (gal) is approximately equal to 3.75 Liters (L)
1 gal ≈ 3.75 L
1 gallon (gal) is equal to 4 quarts (qt)
1 gal = 4 qt
1 quart (qt) is equal to 2 pints (pt)
1 qt = 2 pt
Weight is a measure of how heavy things are.
Here are some common weight conversions we use every day:
Weight Conversions
1 kilogram (kg) is equal to 1000 grams (g)
1 kg = 1000 g
1 gram (g) is equal to 1000 milligrams (mg)
1 g = 1000 mg
1 kilogram (kg) is approximately equal to 2.2 pounds (lb)
1 kg ≈ 2.2 lb
We are able to convert between different units of measurement using a few different methods.
This lesson will show you how to solve using conversion factors, as well as solving by setting up an equation with a constant ratio.
Conversion Factors
In order to convert between units, we need to know the conversion factor.
A conversion factor tells us how much of one type of unit is included in another, for example: 1 kilogram (kg) is equal to 1000 grams (g). We can create two conversion factors:
Depending on what unit we are converting to, we will pick either the first or second conversion factor.
Example: Converting Units Using Conversion Factors
Let's take a look at how to convert 5 kilograms into grams using the conversion factor method.
Step 1  Our general rule is that we will multiply our starting value by the conversion factor with the unit we want to get rid of being on the bottom of the fraction. Since we are converting from kilograms to grams, we will multiply 5 kg by the conversion factor with kilograms on the bottom.
Step 2  This allows us to cancel out the kilograms unit and will give us our answer in grams.
Step 3  Our problem becomes easier to solve when we deal with our units first. All we need to do now is multiply 5 by 1000.
Final answer  5 kilograms are equal to 5000 grams.
Here are two conversion factors for miles to feet.
If we want to convert 3 miles into feet, should we multiply 3 miles by the first conversion factor or the second?
Since we are trying to get rid of the miles unit, we would multiply by the second conversion factor because miles is on the bottom of the fraction.
Converting using conversion factors is one of the easiest ways to convert. Sometimes however, we will have to multiply by a few conversion factors.
Unit conversions involving multiple steps
Example: Unit Conversion Involving Multiple Steps
Let's convert 3 gallons into pints.
If we had the conversion factor from gallons to pints, this would be a one step problem. To illustrate the multiple steps, we are given this information:
1 gal = 4 qt
1 qt = 2 pt
Since we don't have the conversion factor from gallons to pints, we will first convert our 3 gallons into quarts, and then we will convert the number of quarts into pints.
Step 1  Let's convert 3 gallons into quarts. To do so, we multiply 3 gallons by the conversion factor with the gallons unit on the bottom of the fraction.
Step 2  We will cancel the gallons unit (gal) and multiply 3 by 4 in order to get the number of quarts (qt)
Step 3  3 gallons is equal to 12 quarts.
Step 4  To convert 12 quarts into pints, we will multiply 12 quarts by the conversion factor with quarts on the bottom of the fraction.
Step 5  We will cancel the quarts unit (qt). 12 quarts are equal to 24 pints.
Final answer  We successfully converted 3 gallons into 24 pints.
Converting Using Constant Ratios
Another way to convert between different units is to set up a constant ratio across an equation.
Example: Converting with Constant Ratio
Let's take a look at how to convert 45 meters to centimeters using this method
Step 1  Our first step is to create a fraction with our problem. The question mark represents our variable that we are trying to solve for. We can change it to any other variable we like if we wanted to.
Step 2  We then set this fraction equal to the conversion factor with the same units on top and bottom of the fraction.
Step 3  To solve our problem, we need to cross multiply. When we cross multiply we multiply both sides by the denominators. Assuming we correctly set up step 2 so that our units on top and bottom are the same, we can ignore the units at this point because we can cancel them out later.
Step 4  We will move the denominators to the other side and multiply by the numerators.
Step 5  Simplify our answer. 45 times 100 is 4500, and 1 times our variable is equal to one of our variable.
Final Answer  Our final answer is that 45 meters is equal to 4500 centimeters.

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