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Lesson 1.06 Unit Conversion System of Measurements English System Metric System -Volume measured in quarts, cups, gallons -Mass measured in pounds and ounces System of measures - Volume measured in liters -Mass measured in grams -Distance measured in inches, yards, feet, miles -Distance measured in meters -hard to convert form one unit to another -Easy to convert Unit Conversions • Dimensional Analysis: -A problem-solving method used in physics, chemistry, engineering, and mathematics that is based on treating units in calculations as algebraic factors or fractions. -A way to set up math problems; unit conversions. -Sets up multiplication and division in fraction forms. Steps in Unit conversion Example: How many minutes are in 2 days? 1)What are you looking for? • What unit do you want to have for your answer? This is usually given in the problem or question being asked. - 2 days and number of minutes 2) What do you already know? • What equalities or conversions do you already know that might help you solve the Steps problem? Don’t forget that you know the metric prefixes and their relationship to each base unit. • Each step in the setup is its own conversion. The numerator must be equal to the denominator. - 1 day = 24 hours; 1hour = 60 minutes 3) Where does the information go? • Start with the given amount and its unit Steps and use equalities until all the units cancel except the unit you need for your final answer. • Every equivalent can be flipped(1 hr/60 mins or 60 mins/ 1 hr)—be sure to keep each number with its correct unit, but you can switch which one is in the numerator and which one is in the denominator. - 2 days x 24 hrs/1 day x 60 mins/ 1 hr Steps 4) Solve it! • You multiply everything that is on top (numerators). • Then divide by everything that is on the bottom (denominators) to get the number that goes in your answer. - Numerator(top) = 2 x 24 x 60 = 2880 Denominator (bottom)= 1 x 1 = 1 - 2880/1 = 2880 minutes Sample Problem A)If your dog weighs 40 kilograms, how many milligrams does it weigh? Step 1- 40 kg and number of milligrams(mg) Step 2- 1 kg = 10^3 g ; 10^-3g = 1 mg Step 3- 40 kg x 10^3 g/1 kg x 1 mg/10^-3 g Step 4- (top)40 x 10^3 x 1 = 40000 (bottom)1 x 10^-3 = 0.001 40000/0.001 = 40,000,000 mg Sample Problem B)Change the measurement 150 mm to dam Step 1 -150 mm and unit dam Step 2 - 1 mm = 10^-3 m ; 1 dam = 10^1 m Step 3 - 150 mm x 10^-3 m/1mm x 1 dam/ 10^1 m Step 4 - 150 x 10^-3 x 1 / 1 / 10^1 = 0.015 dam Sample Problem C) Convert 6.5 cm/s to m/hr(unit is a fraction) Step 1- 6.5 cm/s and m/hr Step 2-1 m = 100 cm ; 1 hr = 60 mins ; 1 min = 60 secs Step 3- (convert numerator first) 6.5 cm/s x 1 m/100 cm = 0.065 - you can start with the numerator first. The one sec is still in the denominator, but you can ignore it until you get cm converted to m. Sample Problems - now you can continue the problem by changing the denominator from s to hr. (convert denominator) 0.065 m/s x 60 s/1 min x 60 min/1 hr Step 4 – (top)0.065 x 60 x 60 = 234 (bottom) 1 x 1 = 1 234 / 1 = 234 m/hr Sample Problem D) Convert the density 6.2 g/mL to kg/L Step 1 - 6.2 g/mL and unit kg/L Step 2 – 1000 g = 1 kg ; 1 L = 1000 mL Step 3 – 6.2 g/mL x 1kg/1000 g x 1000 mL/ 1L Step 4 – 6.2 x 1 x 1000 / 1000 / 1 = 6.2 kg/L