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Units are a way in which we agree on describing different measurements. The only reason that units even exist is because humanity has collectively decided that it is very convenient to have standards of measurement!

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The two systems of measurement that you should be familiar with are

- United States Customary System
- International System of Units (often called SI or referred to as Metric)

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There are 7 units that scientists and mathematicians are the most interested describing:

- Length
- Time
- Amount of something
- Electric current
- Temperature
- Luminous intensity
- Mass

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For our purposes, we are mostly interested in Length, Time, Temperature, and Mass, since the other 3 units are usually reserved for more scientific courses such as Chemistry and Physics.

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For the United States Customary System, length is most often measured in inches, feet, yards, and miles.

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In the SI system, length is most often measured in millimeters, centimeters, meters, and kilometers.

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You will not be expected to convert between Customary and SI units unless you are explicitly given the conversion ratio. For example, a test would not ask you to convert 5 inches to centimeters without telling you that 1 inch = 2.54 centimeters.

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You should be familiar with unit conversions within a single system of measurement. The following table gives conversion ratios between units.

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To apply this knowledge to a problem, we will use equivalent values to determine how to correctly change between units. Suppose a cross-country team ran 5 miles as part of their training. How many feet did the cross country team run that day?

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We want to use a ratio that equates feet to miles, so we use 5,280 feet = 1 mile.

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Simply multiply both sides of this equation by 5 to find that 26,400 feet = 5 miles.

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Therefore, the cross-country team ran 26,400 feet!

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Time is measured with the same units for the Customary and SI system. These units should be very familiar to you since they affect almost everything you do on a daily basis!

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The following table lists some of the most common conversions for time.

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This is particularly useful when trying to determine how many smaller units are in a specific amount of time. Consider how many minutes are in a year. You may already know the answer from a popular musical called Rent, but we’ll calculate it here once more!

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First, convert 1 year into the smallest unit we can. This means that 1 year = 365 days.

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Now, we must convert 365 days into hours. Multiply 365 days by 24 hours in a day to find that there are 8,760 hours in a year.

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Finally, we convert hours to minutes by multiplying 8,760 hours by 60 minutes in an hour.

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This shows us that there are a total of 525,600 minutes, which is the exact same as the song from the musical Rent!

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Remember to always write out your units when you convert between units, so that you can verify they cancel at every step along the way. This will prevent basically every common error that occurs on tests.

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Temperature

Temperature is actually measured in three common units! The Customary system typically uses Fahrenheit while most of the world uses Celsius. However, the SI unit for temperature is actually Kelvin, which is used most commonly for scientific studies.

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The major points on each scale that you should be familiar with are the temperature at which water freezes and the temperature at which water boils.

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To convert from Celsius to Kelvin, simply add 273 to the value in degrees Celsius. This is due to the fact that Kelvin reserves its 0 to represent absolute 0, which is the lowest temperature theoretically possible! This means that 0 Kelvin = -273 °C, which is another measurement for absolute zero.

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Converting from Fahrenheit to Celsius requires a specific formula:

C = (F - 32) * 5/9

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You are not expected to memorize this formula, though you may see it often enough that you end up having it memorized! To use this, simply substitute the temperature in Fahrenheit and then solve for the temperature in degrees Celsius.

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If the temperature outside is 41 degrees fahrenheit, we have the following equation Celsius = (41 - 32) * (5/9).

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This gives us that degrees Celsius = 9 degrees times 5/9 and degrees Celsius = 5 degrees.

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To convert from Celsius to Fahrenheit, we simply solve the earlier formula for Fahrenheit and then do the same procedure. This gives the following formula: F =(9/5)C + 32.

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Be sure to have the freezing and boiling points of water memorized for both Fahrenheit and Celsius as this is the most important part of measuring temperature.

Mass

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Finally, we will discuss the units and conversions for mass.

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The Customary system measures mass in terms of ounces, pounds, and tons.

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The SI units for mass are milligrams, grams, kilograms, and metric tons.

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To convert between these units, use the following table.

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Some common references for these weights are that a gram is approximately the weight of a paperclip and a car weighs around 2 tons.

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You may also be given that 1 kilogram approximately equals 2.2 pounds to convert between the two systems of measurement.

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Suppose that a certain truck weighs 10,000 pounds with its cargo included. The truck only weighs 6,000 pounds without its cargo. How many tons of cargo is the truck carrying?

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To solve this problem, we first subtract the weight of the truck from the total weight. This shows us that there is 10,000 - 6,000 = 4,000 pounds of cargo.

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Convert pounds to tons by multiplying 4,000 pounds * (1 ton / 2,000 pounds) = 2 tons.

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The same sort of conversions can be performed on SI Units.

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The most important thing to remember when converting between units is to include the name of each unit as you multiply. It is incredibly common to not know whether to multiply by 60 or divide by 60 when you are trying to convert from seconds to minutes and you don’t want to be guessing on an exam! Always, always, always write out the name of the units and place them in a fraction to see how your units are actually cancelling.

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