Basic Math and Pre-Algebra - Measurements - Quick Guides | Mathematics

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Study GuideBasic Math and Pre-Algebra–Measurements1. Metric System1.1What Is the Metric System?Themetric systemis a system of measurement based onpowers of ten.That means everything is built around multiples of 10—which makes it simple and organized.To understand the metric system, you need to know what theprefixesmean. Prefixes are smallwords added to the beginning of a unit (like meter or gram) to show how big or small something is.1.2Metric PrefixesHere are the most common prefixes you need to know:•kilo= thousand (1,000)•hecto= hundred (100)•deka= ten (10)•deci= tenth (1/10)•centi= hundredth (1/100)•milli= thousandth (1/1,000)Notice the pattern:•Prefixes above the base unit meanlarger amounts.•Prefixes below the base unit meansmaller amounts.Because everything is based on powers of ten, conversions are much easier than in other systems.

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Study Guide1.3Applying Prefixes to LengthThe base unit for length is themeter (m).Here’s how the prefixes change it:•1 kilometer (km) = 1,000 meters•1 hectometer (hm) = 100 meters•1 dekameter (dkm) = 10 meters•10 decimeters (dm) = 1 meter•100 centimeters (cm) = 1 meter•1,000 millimeters (mm) = 1 meterSo moving between units is just multiplying or dividing by 10, 100, or 1,000.1.4Applying Prefixes to VolumeThe base unit for volume is theliter (L or l).•1,000 milliliters (mL or ml) = 1 liter•1,000 liters = 1 kiloliter (kL or kl)Again, everything changes by powers of 10.1.5Applying Prefixes to MassThe base unit for mass is thegram (g).•1,000 milligrams (mg) = 1 gram•1,000 grams = 1 kilogram (kg)•1,000 kilograms = 1 metric ton (t)Just like length and volume, the pattern stays consistent.

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Study Guide1.6Helpful ApproximaƟonsIt can also help to compare metric units to familiar U.S. customary units:•Ameteris a little more than a yard.•Akilometeris about 0.6 mile.•Akilogramis about 2.2 pounds.•Aliteris slightly more than a quart.These comparisons help you estimate measurements in real life.1.7Why the Metric System Is Easy to UseThe biggest advantage of the metric system is its simplicity:• Everything is based on powers of 10• Conversions only require moving the decimal point• The same prefixes work for length, mass, and volumeOnce you learn the prefixes, you can measure almost anything!SummaryThe metric system is based on powers of ten, which makes conversions simple and consistent.Key prefixes:•kilo = 1,000•hecto = 100•deka = 10•deci = 1/10•centi = 1/100•milli = 1/1,000

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Study GuideBase units:•Length→meter•Volume→liter•Mass→gramConversions always involve multiplying or dividing by 10, 100, or 1,000.Because the system follows a clear pattern, it is easier to learn and use than many othermeasurement systems.2. ConverƟng Units of MeasureConverting units means changing one type of measurement into another—like yards to inches orpounds to kilograms.There are two main ways to solve conversion problems:1.Use what you already know (basic multiplication or division).2.Set up a proportion and solve it.Example 1:Yards to InchesQuestion:If 36 inches equal 1 yard, how many inches are in 3 yards?Method 1: Think it throughIf 1 yard = 36 inches,then 3 yards = 3 × 36.So,3 yards = 108 inches.

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Study GuideMethod 2: Use a ProportionSet up matching units across from each other:Cross multiply:So,x = 108 inches.✔Always place the same units across from each other (inches with inches, yards with yards).Example 2:Pounds to KilogramsQuestion:If 2.2 pounds equal 1 kilogram, how many kilograms are in 10 pounds?Step 1: Think about itDivide 10 by 2.2:So the answer should be about4.5 kilograms.Step 2: Solve Using a ProportionSet up kilograms over pounds:Cross multiply:

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Study GuideDivide:Rounded to the nearest tenth:Example 3:Decades to WeeksQuestion:How many weeks are in 3 decades?Step 1: Convert decades to years1 decade = 10 years3 decades = 30 yearsStep 2: Convert years to weeks1 year = 52 weeksSo,3 decades = 1,560 weeks.One-Step MethodYou can also do it in one calculation:Example 4:Miles to YardsQuestion:If 1 mile equals 1,760 yards, how many yards are in 5 miles?

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Study GuideMultiply:So,5 miles = 8,800 yards.Example 5:Kilometers to DekametersQuestion:If 1 kilometerequals 1,000 meters, and 1 dekameter equals 10 meters, how many dekameters are in3 kilometers?Step 1: Convert kilometers to meters1 km = 1,000 m3 km = 3,000 mStep 2: Convert meters to dekameters1 dekameter = 10 metersSet up the proportion:Cross multiply:Divide:So,3 kilometers = 300 dekameters.2.2Reminders for Conversions• Keep matching units across from each other in proportions.• Multiply when converting to smaller units.• Divide when converting to larger units.• Check if your answer makes sense.

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Study GuideFor example:•More yards should mean more inches.•More miles should mean more yards.SummaryUnit conversions help us change measurements from one unit to another.To solve:•Use multiplication or division when possible.•Or set up a proportion and cross multiply.Examples covered:•3 yards = 108 inches•10 pounds≈4.5 kilograms•3 decades = 1,560 weeks•5 miles = 8,800 yards•3 kilometers = 300 dekametersThe most important rule:Keep units organized and match them correctly.With practice, unit conversions become much easier and faster to solve.3. Quiz: U.S. Customary System, Metric System, and ConverƟng Unitsof Measure1. QuestionOne mile is the same asAnswer Choices•1,560 yards•5,280 feet•53,360 inches

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Study GuideCorrect Answer࿨࿩࿪5,280 feetWhy This Is CorrectOne mile equals 5,280 feet in the customary (U.S.) system of measurement.Since 1 yard equals 3 feet, one mile (1,760 yards) equals 1,760 × 3 = 5,280 feet.This is a standard distance conversion used in the U.S.2. QuestionOne square yard is the same asAnswer Choices•3 square feet•6 square feet•9 square feetCorrect Answer࿨࿩࿪9 square feetWhy This Is CorrectOne yard equals 3 feet.When converting square units, you must multiply both dimensions:3 feet × 3 feet = 9 square feet.So, one square yard equals 9 square feet.3. Question1,000 pounds is the same as

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Study GuideAnswer Choices•1,600 ounces•1/2 ton•1 tonCorrect Answer࿨࿩࿪1/2 tonWhy This Is CorrectIn the U.S. system, 1 ton equals 2,000 pounds.So, 1,000 pounds is half of 2,000 pounds.Therefore, 1,000 pounds equals 1/2 ton.4. Question1 gallon = ____ quartsAnswer Choices•2•4•6Correct Answer࿨࿩࿪4Why This Is CorrectIn the customary system, 1 gallon equals 4 quarts.This is a basic liquid measurement conversion.

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