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The Student Success Commons at York County Community College: Units and Conversions

Units and Conversions 101

UNITS

• The units of a quantity describe what the quantity measures or counts. Units provide crucial context. For example, if you ask a car mechanic how long it will take to have your radiator fixed and they say "5" you need the units to fully understand their meaning. Is it 5 minutes, 5 hours, 5 days, 5 weeks, 5 months? 
• Unit analysis (also called dimensional analysis) is the process of working with units to help solve problems.
• You can cancel units that appear in the top and bottom of one fraction, or in the top of one fraction and in the bottom of another as long as the two fractions are being multiplied (see the Unit analysis (cancelling units) PDF)
• Tip: You generally cannot add or subtract numbers with different units. For example, you couldn't add 3 inches and 5 miles to get 8; what would the unit be? But you can combine different units by converting at least one of the units. (Using the previous example, if we converted 5 miles into inches, we could then add the two values because they would both have the same unit: inches.)
 

CONVERSIONS

• When you are trying to add or subtract two quantities and the units are not the same you will need to convert at least one of the units.
• A conversion factor is used to change the units of a measured quantity without changing its value. Common conversion factors and how to use them are given on this page, as are additional resources and examples.

Metric units

The metric system is a system of measurement that uses the meter, liter, and gram as base units of length (distance), capacity (volume), and weight (mass) respectively. 
 

LENGTH Meter (m)
MASS Gram (g)
VOLUME Liter (L)

Metric system prefixes tell you how much bigger or smaller a unit is than the base unit. These prefixes are all powers of 10, which makes converting from one metric measurement to another very simple. Here are some common prefixes.

KILO: 1,000 × Base
HECTO: 100 × Base
DECA: 10 × Base
[BASE]
DECI: 0.1 × Base
CENTI: 0.01 × Base
MILLI: 0.001 × Base
MICRO: 0.000001 × Base

Metric to metric conversions

One of the biggest advantages that the metric system offers is that its units scale by powers of 10. Because of this, converting within metric measurements is usually as easy as multiplying or dividing a given measurement by a power of 10 to find the new value (or, as a shortcut, simply moving its decimal point). Here are some examples, but we encourage you to examine the general process and practice converting metric to metric on your own to get the hang of the procedure.

TO CONVERT TO OPERATION BECAUSE
kilometers meters divide by 1,000 meters is 3 steps down from kilometers
kilometers centimeters divide by 100,000 centimeters is 5 steps down from kilometers
meters decameters multiply by 10 decameters is one step up from meters
grams kilograms divide by 1,000 grams is 3 steps down from kilograms

Metric to Imperial (U.S.) conversions (and vice versa)

LENGTH

TO CONVERT TO OPERATION
centimeters inches divide by 2.54
meters inches multiply by 39.37
meters feet multiply by 3.281
meters yards multiply by 1.094
meters miles divide by 1609.34
kilometers miles divide by 1.6093

 

MASS

TO CONVERT TO OPERATION
grams ounces divide by 28.3495
kilograms ounces multiply by 35.274
pounds grams multiply by 453.592
kilograms pounds multiply by 2.205
kilograms tons divide by 907.184

VOLUME

TO CONVERT TO OPERATION
milliliters teaspoon divide by 4.92892 (some texts just use 5)
milliliters tablespoon divide by 14.7868 (some texts just use 15)
liter fluid ounce multiply by 33.814
liter cup multiply by 4.167
liter gallon divide by 3.78541178


**Please round as required by your specific course.

Temperature

TO CONVERT TO FORMULA
Celsius (C) Fahrenheit (F) Multiply by 1.8, then add 32

i.e., F = 1.8C + 32
Fahrenheit (F) Celsius (C) Subtract 32, then divide by 1.8

i.e., C = (F - 32)/1.8
Celsius (C) Kelvin (K) add 273.15

i.e., K = C + 273.15
Fahrenheit (F) Kelvin (K) Subtract 32, then divide by 1.8, then add 273.15

i.e., K = (F - 32)/1.8 +273.15

Time

  • SECOND
    • 60 seconds = 1 minute
    • 3,600 seconds = 1 hour
    • 86,400 seconds = 1 day
  • MINUTE
    • 60 minutes = 1 hour
    • 1,440 minutes = 1 day
    • 10,080 minutes = 1 week
  • HOUR
    • 24 hours = 1 day
    • 168 hours = 1 week
  • DAY
    • 7 days = 1 week
    • 365 days = 1 year
  • WEEK
    • 4 weeks =  1 month
    • 52 weeks = 1 year
  • MONTH
    • 12 months = 1 year
  • YEAR
    • 10 years =  1 decade
Review and practice converting units of time at Khan Academy

Trigonometry Units

There are various ways to measure angles:

  • Degrees: there are 360° in a circle
  • Radians: there are 2π radians in a circle
  • Minutes: there are 21,600 minutes in a circle
  • Seconds: There are 1,296,000 seconds in a circle

 

Note: the minutes and seconds used in trigonometry do not refer to measures of time, they refer to angle measurements.

Imperial (U.S. customary) units

LENGTH
  • inches (in)
  • feet (ft)
  • yards (yd)
  • miles (mi)

MASS
  • ounce (oz)
  • pound (lb)
  • ton (t)

VOLUME
  • teaspoons (tsp)
  • tablespoons (tbsp)
  • cups (c)
  • pints (pt)
  • quarts (qt)
  • gallons (gal)

Imperial to imperial conversions

LENGTH

TO CONVERT TO OPERATION
inches feet divide by 12
inches yards divide by 36
feet yards divide by 3
square feet square yards divide by 9
cubic feet cubic yards divide by 27
feet miles divide by 5280
yards miles divide by 1760

 

MASS

TO CONVERT TO OPERATION
ounces pounds divide by 16
pounds tons divide by 2000

 

VOLUME

TO CONVERT TO OPERATION
teaspoon tablespoon divide by 3
tablespoon fluid ounce divide by 2
fluid ounce cup divide by 8.115
cup pint divide by 1.972
pint quart divide by 2
quart gallon divide by 4


**Please round as required by your specific course.

Imperial (U.S.) to Metric conversions **

LENGTH

TO CONVERT TO MULTIPLY BY
inches centimeters 2.54
inches meters 0.0254
feet meters 0.3048
yards meters 0.9144
miles meters 1609.34
miles kilometers 1.6093

 

MASS

TO CONVERT TO MULTIPLY BY
ounces grams 28.3495
ounces kilograms 0.0283
pounds grams 453.592
pounds kilograms 0.453592
tons kilograms 907.184

 

VOLUME

TO CONVERT TO MULTIPLY BY
teaspoon milliliters 4.92892 (some texts just use 5)
tablespoon milliliters 14.7868 (some texts just use 15)
fluid ounce liter 0.02957353
cup liter 0.23658824
gallon liter 3.78541178


**Please round as required by your specific course.

Video tutorials

Trigonometry conversions

TO CONVERT TO MULTIPLY BY
degrees radians (π ÷ 180°)
radians degrees (180° ÷ π)
degrees minutes 60
degrees seconds 3,600
minutes seconds 60
minutes degrees (1 ÷ 60)
seconds degrees (1 ÷ 3,600)

 

 

 

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Room 201
ycccssc@mainecc.edu
207-216-4300


  

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