Measurement: Cheat Sheet

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Essential Concepts

  • Conversion factors are special numbers or ratios that help you convert between different units of measurement. They allow you to change a measurement from one unit to another by multiplying or dividing it by the conversion factor.
  • Common Customary Conversions
    • [latex]1[/latex] ft = [latex]12[/latex] inches
    • [latex]1[/latex] yard = [latex]3[/latex] feet
    • [latex]1[/latex] mile = [latex]5,280[/latex] feet
    • [latex]1[/latex] pound = [latex]16[/latex] ounces
    • [latex]1[/latex] ton = [latex]2,000[/latex] pounds
    • [latex]1[/latex] cup = [latex]8[/latex] fluid ounces
    • [latex]1[/latex] pint = [latex]2[/latex] cups
    • [latex]1[/latex] quart = [latex]2[/latex] pints
    • [latex]1[/latex] quart = [latex]4[/latex] cups
    • [latex]1[/latex] gallon = [latex]4[/latex] quarts
    • [latex]1[/latex] gallon = [latex]16[/latex] cups
  • When you have measurements in different units and need to solve problems involving them, you can convert the measurements to a single unit using conversion factors. This helps you compare or combine the measurements easily.
  • Approximate conversions between Metric and Customary
    • [latex]1[/latex] centimeter is a little less than half an inch
    • [latex]1.6[/latex] kilometers is about [latex]1[/latex] mile
    • [latex]1[/latex] meter is about [latex]3[/latex] inches longer than [latex]1[/latex] yard
    • [latex]1[/latex] kilogram is a little more than [latex]2[/latex] pounds
    • [latex]28[/latex] grams is about the same as [latex]1[/latex] ounce
    • [latex]1[/latex] liter is a little more than [latex]1[/latex] quart
    • [latex]4[/latex] liters is a little more than [latex]1[/latex] gallon
  • The names of metric units are formed by adding a prefix to the basic unit of measurement.
    • kilo- = [latex]1,000[/latex] times larger than the base unit
    • hecto- = [latex]100[/latex] times larger than the base unit
    • deka- = [latex]10[/latex] times larger than the base unit
    • meter, gram, liter = base units
    • deci- = [latex]10[/latex] times smaller than the base unit
    • centi- = [latex]100[/latex] times smaller than the base unit
    • milli- = [latex]1,000[/latex] times smaller than the base unit
  • Measuring mass in the metric system
    • [latex]1[/latex] kilogram = [latex]1,000[/latex] grams
    • [latex]1[/latex] hectogram = [latex]100[/latex] grams
    • [latex]1[/latex] dekagram = [latex]10[/latex] grams
    • [latex]1[/latex] gram = [latex]1[/latex] gram
    • [latex]1[/latex] decigram = [latex]0.1[/latex] gram
    • [latex]1[/latex] centigram = [latex]0.01[/latex] gram
    • [latex]1[/latex] milligram = [latex]0.001[/latex] gram
  • Measuring distance in the metric system
    • [latex]1[/latex] meter = [latex]1,000,000[/latex] micrometers
    • [latex]1[/latex] meter = [latex]1,000[/latex] millimeters
    • [latex]1[/latex] meter = [latex]100[/latex] centimeters
    • [latex]1[/latex] meter = [latex]10[/latex] decimeters
    • [latex]1[/latex] dekameter = [latex]10[/latex] meters
    • [latex]1[/latex] hectometer = [latex]100[/latex] meters
    • [latex]1[/latex] kilometer = [latex]1,000[/latex] meters
    • [latex]1[/latex] megameter = [latex]1,000,000[/latex] meters
  • To solve real world conversion these problems, the first step is understanding the context and using clues from the problem to determine the appropriate conversions. Additionally, when performing calculations with mixed units in the metric system, we still need to be careful and ensure that we are adding or subtracting similar units.
  • Conversions between U.S. and metric measuring systems
    • [latex]3.28[/latex] feet in a meter
    • [latex]2.54[/latex] centimeters in an inch
    • [latex]2.2[/latex] pounds in a kilogram
    • [latex]3.785[/latex] liters in a gallon
  • Temperature conversions between Celsius and Fahrenheit can be used with the following formulas:
    • [latex]C=\dfrac{5}{9}(F-32)[/latex]
    • [latex]F=\dfrac{9}{5}C+32[/latex]
  • Proportions are a useful tool for solving problems that involve rates and ratios. We can set up proportions by equating two rates or ratios, helping us find unknown values and understand relationships between different quantities.
  • Ratios compare two quantities or measures, and they can be written in different ways, like “a to b,” “a:b,” or “a/b.” Rates are a special type of ratio that compares measurements with different units, like miles and hours.
  • Proportions are equations that show the equality of two rates or ratios. They have two important properties: First, the cross products (the product of the means and the product of the extremes) are always equal. Second, if a/b = c/d, then b/a = d/c. This second property allows us to write the reciprocal of a proportion.
  • Dimensional analysis is a method that helps us convert measurements from one unit to another. It involves using conversion factors, which are ratios that tell us how many of one unit is equal to another. By multiplying our original measurement by these conversion factors, we can change the units until we reach the desired unit.

Glossary

capacity

the amount of liquid (or other pourable substance) that an object can hold when it’s full

dimensional analysis

a method used to convert from one unit to another

length

the distance from one end of an object to the other end or from one object to another

metric system

a base [latex]10[/latex] system that uses the base units meter, liter, and gram to measure length, liquid volume, and mass

proportion

an equation showing the equivalence of two rates or ratios

rate

a specific kind of ratio in which two measurements with different units are related to each other

ratio

a comparison between two quantities or measures

weight

how heavy or light an object is

Key Equations

Celsius measurement to a Fahrenheit measurement

[latex]F=\dfrac{9}{5}C+32[/latex]

Fahrenheit measurement to a Celsius measurement

[latex]C=\dfrac{5}{9}(F-32)[/latex]