Common Weights and MeasuresCommon Weights and Measures

Length

Metric System

1 millimeter = 1/1,000 meter

1 centimeter = 1/100 meter

1 decimeter = 1/10 meter

1 meter (basic unitof length)

1 dekameter = 10 meters

1 kilometer = 1,000 meters

American and British Units

1 inch = 1/36 yard = 1/12 foot

1 foot = 1/3 yard

1 yard (basic unit of length)

1 rod = 5 1/2 yards

1 furlong = 220 yards = 40 rods

1 mile = 1,760 yards = 5,280 feet

1 fathom = 6 feet

1nautical mile = 6,076.1 feet

Conversion Factors

1 centimeter = 0.39 inch

1 inch = 2.54 centimeters

1 meter = 39.37 inches

1 foot = 0.305 meter

1 meter = 3.28 feet

1 yard = 0.914 meter

1 meter = 1.094 yards

1 kilometer = 0.62 mile

1 mile = 1.609 kilometers

Area

Metric System

1 square centimeter = 1/10,000 square meter

1 square decimeter = 1/100 square meter

1 square meter (basic unit of area)

1 are = 100 square meters

1 hectare = 10,000 square meters = 100 ares

1 square kilometer = 1,000,000 square meters

American and British Units

1 square inch = 1/1,296 square yard = 1/144 square foot

1 square foot = 1/9 square yard

1 square yard (basic unit of area)

1 square rod = 30 1/4 square yards

1 acre = 4,840 square yards = 160 square rods

1square mile = 3,097,600 square yards = 640 acres

Conversion Factors

1 square centimeter = 0.155 square inch

1 square inch = 6.45 square centimeters

1 acre = 0.405 hectare

1 hectare = 2.47 acres

1 square kilometer = 0.386 square mile

1 square mile = 2.59 square kilometers

Volume and Capacity (Liquid and Dry)

Metric System

1 cubic centimeter = 1/1,000,000 cubic meter

1 cubic decimeter = 1/1,000 cubic meter

1 cubic meter = 1 stere (basic unit of volume)

1 milliliter = 1/1,000 liter = 1 cubic centimeter

1 centiliter = 1/100 liter

1 deciliter = 1/10 liter

1 liter = 1 cubic decimeter (basic unit of capacity)

1 dekaliter = 10 liters

1 hectoliter = 100 liters = 1/10 cubic meter

American and British Units

1 cubic inch = 1/46,656 cubic yard = 1/1,728cubic foot

1 cubic foot = 1/27 cubic yard

1 cubic yard (basic unit of volume)

1 U.S.fluid ounce = 1/128 U.S. gallon = 1/16 U.S. pint

1 British imperial fluid ounce = 1/160 imperial gallon = 1/20 imperial pint

1 pint = 1/8 gallon = 1/2 quart

1 quart = 1/4 gallon

1 U.S. gallon (basic unit of liquid capacity in theUnited States) = 231 cubic inches

1 imperial gallon (basic unit of liquid capacity in some Commonwealth nations) = 277.4 cubic inches

1 dry pint = 1/64 bushel = 1/2 dry quart

1 dry quart = 1/32 bushel = 1/8 peck

1 peck = 1/4 bushel

1 U.S. bushel (basic unit of dry capacity in the United States) = 2,150.4 cubic inches

1 imperial bushel (basic unit of dry capacity in some Commonwealth nations) = 2,219.4 cubic inches

Conversion Factors

1 cubic centimeter = 0.06 cubic inch

1 cubic inch = 16.4 cubic centimeters

1 cubic yard = 0.765 cubic meter

1 cubic meter = 1.3 cubic yards

1 milliliter = 0.034 fluid ounce

1 fluid ounce = 29.6 milliliters

1 U.S. quart = 0.946 liter

1 liter = 1.06 U.S. quarts

1 U.S. gallon = 3.8 liters

1 imperial gallon = 1.2 U.S. gallons = 4.5 liters

1 liter = 0.9 dry quart

1 dry quart = 1.1 liters

1 dekaliter = 0.28 U.S. bushel

1 U.S. bushel = 0.97 imperial bushel = 3.5 dekaliters

Weight (Mass)

Metric System

1 milligram = 1/1,000,000 kilogram = 1/1,000 gram

1 centigram = 1/100,000 kilogram = 1/100 gram

1 decigram = 1/10,000 kilogram = 1/10 gram

1 gram = 1/1,000 kilogram

1 dekagram = 1/100 kilogram = 10 grams

1 hectogram = 1/10 kilogram = 100 grams

1 kilogram (basic unit of weight or mass)

1 metric ton = 1,000 kilograms

American and British Units: Avoirdupois

1 grain = 1/7,000 pound = 1/437.5 ounce

1 dram = 1/256 pound = 1/16 ounce

1 ounce = 1/16 pound

1 pound (basic unit of weight or mass)

1 short hundredweight = 100 pounds

1 long hundredweight = 112 pounds

1 short ton = 2,000 pounds

1 long ton = 2,240 pounds

American and British Units: Troy and Apothecaries'

1 grain = 1/7,000 avoirdupois pound = 1/5,760 troy or apothecaries' pound

1 apothecaries' scruple = 20 grains = 1/3 dram

1 pennyweight = 24 grains = 1/20 troy ounce

1 apothecaries' dram = 60 grains = 1/8 apothecaries' ounce

1 troy or apothecaries' ounce = 480 grains = 1/12 troy or apothecaries' pound

1 troy or apothecaries' pound = 5,760 grains = 5,760/7,000 avoirdupois pound

Conversion Factors

1 milligram = 0.015 grain

1 grain = 64.8 milligrams

1 gram = 0.035 avoirdupois ounce

1 avoirdupois ounce = 28.35 grams

1 troy or apothecaries' pound = 0.82 avoirdupois pound = 0.37 kilogram

1 avoirdupois pound = 1.2 troy or apothecaries' pounds = 0.45 kilogram

1 kilogram = 2.205 avoirdupois pounds

1 short ton = 0.9 metric ton

1 metric ton = 1.1 short tons

Read more:Common Weights and Measures (table) | Infoplease.comhttp://www.infoplease.com/encyclopedia/science/common-weights-measures-table.html#ixzz2uhY0EGfV

Measurement: OverviewThere are two basicsystems of measurement. When measuring in these systems, a comparison is made to some unit recognized as a standard. The system used in the United States is called thecustomary systemof measurement.Theunits of measurein the customary system are:Customary System

LENGTH

1 foot (ft)=12 inches (in.)

1 yard (yd)=3 feet

1 yard=36 inches

1 mile=1,760 yards

1 mile=5,280 feet

WEIGHT

1 pound (lb)=16 ounces (oz)

1 ton (T)=2,000 pounds

CAPACITY

1 pint (pt)=2 cups

1 quart (qt)=2 pints

1 quart=4 cups

1 gallon (gal)=4 quarts

The otherbasic systemof measurement is called themetric system,or SI (International Systemof Units). It was first adopted in France and is currently used by approximately 95% of the world's population. Liberia and Myanmar (Burma) are the only other countries besides the United States that have not officially adopted the metric system.Within the metric system, themeteris the fundamental unit of length; thegramis the fundamental unit of mass, and theliteris the fundamental unit of capacity. The metric system is a base-ten system. Prefixes are used to designate 10 times(deka-),100 times(hecto-),and 1,000 times(kilo-)the unit. The prefixesdeci-, centi-,andmilli-are used to designate,, andof the unit, respectively.Metric System

LENGTH

1 centimeter (cm)=10 millimeters (mm)

1 decimeter (dm)=10 centimeters

1 meter (m)=10 decimeters

1 kilometer (km)=1,000 meters

MASS

1 kilogram (kg)=1,000 grams (g)

CAPACITY

1 liter (L)=1,000 milliliters (mL)

In this chapter, students work with the customary units of measure for length, weight and capacity and then with the metric units for the same attributes. They measure the length of various objects to the nearest inch,inch, andinch. Students review how to find the perimeter of a rectangle, recalling thatperimeteris the distance around a figure and is computed by adding the lengths of the figure's sides.

Students first learned how to find perimeter in second grade. Not until fifth grade, will they be introduced to the formula perimeter = 2l+ 2w.Once they have found the perimeter of a figure, students can multiply or divide to convert feet to inches, feet to yards, yards to feet, and feet and yards to miles. In order to convert, students look up the equivalent values for the two units and then decide whether to multiply or divide. When converting from a larger unit, such as feet, to a smaller unit, such as inches, students multiply. So, to convert 8 feet to inches, students look at the table of equivalencies to find that 1 foot equals 12 inches. Then they multiply the number of feet, 8, by the number of inches in 1 foot, 12, to find that 8 feet = 96 inches.When converting from a smaller unit, such as feet, to a larger unit, such as yards, students divide. To convert 48 feet into yards, students look at the table of equivalencies to find that 1 yard equals 3 feet. They then divide the number of feet, 48, by the number of feet in 1 yard, 3, to find that 48 feet = 16 yards. Students may have difficulty remembering when to multiply and when to divide. If so, have them think about whether there will be more or less of the unit they are converting to than of the unit they are converting from. If there will be more of thenew unit, they must multiply. If there will be less, they must divide.Students will review the customary units of capacity and weight, converting among customary units. Students should be familiar with the measures of cups, pints, quarts, and gallons, and the measures of ounces and pounds. This is the first time they will have worked with tons. As with linear measure, to convert between units of capacity or weight, students must look up the unit equivalencies and then decide whether to multiply or divide.Students review the metric system by actually measuring objects to the nearest centimeter and millimeter. Then they progress to finding perimeter in meters and kilometers and to converting between millimeters, centimeters, decimeters, meters, and kilometers. At this point students will not work with dekameters or hectometers.Converting units within the metric system is much simpler than within the customary system. Because the metric system is a base-ten system, students simply need to multiply or divide by powers of ten to convert. They can look up the equivalencies in the tables provided in their student book. They then multiply or divide by the appropriate power of ten, depending upon whether they are converting from larger units to smaller units or from smaller units to larger units. For example, to convert 5 meters to centimeters, students multiply the number of meters, 5, by the number of centimeters in 1 meter, 100, to find that 5 m = 500 cm. To convert 350 millimeters to centimeters, students divide the number of millimeters, 350, by the number of millimeters in 1 centimeter, 10, to find that 350 mm = 35 cm. Since the same prefixes are used to measure length, capacity, and weight, students may come to understand the relationship between the prefixes and not need to look up the equivalencies.Students progress to converting between metric units of capacity and mass. Although the termsmassandweightare often used interchangeably, they do have different meanings. Mass is the amount of matter in an object. Weight measures the force of the Earth's gravity acting upon the mass of an object. That is why objects in space, being far from Earth and the pull of gravity, are weightless. At this point, you need not make this distinction for students unless they ask about the difference in terms.Students will also multiply or divide by 1,000 to convert between liters and milliliters or between kilograms and grams. At this grade level,milli-andkilo-are the only prefixes that students will work with in measuring capacity and mass, since these are the most common units used in everyday life.Finally, students will study the units of measure for temperature in both the customary and metric systems. They informally compare the two temperature scales by comparing reference points such as the temperatures at which water boils and freezes, normal body temperature, and room temperature. TheFahrenheitthermometer is part of the customary system and is named after Gabriel Daniel Fahrenheit (1686-1736), a famous physicist. This thermometer is graduated so that water freezes at 32 and boils at 212. Normal body temperature is 98.6. The Celsius thermometer, also known as the Centigrade scale, is named after Anders Celsius (1701-1744), a Swedish astronomer, and is one of two metric scales for temperature. The Celsius scale is graduated so that water freezes at 0 and boils at 100. Normal body temperature is 37.Using a drawing of a thermometer, students can find the difference between two temperatures. This will also serve as the students' first introduction to the concept of negative numbers. Students learn that temperatures below zero on either scale are negative temperatures. In dealing with negative numbers, students can think of the thermometer as a number line and can use the drawing of a thermometer to count between temperatures to find the difference. They will not actually subtract to find differences. At this point they will not learn how to subtract integers. Once students have practiced using a thermometer to find differences between temperatures, they will use this skill to solve word problems involving temperatures.