Unit-Conversions.ppt

Metric Units and Conversions  What A unit is ais Unit conversion Conversion? a changing of one unit to another. Unit Examples:  meters  grams  inches  feet  pounds  seconds Any time you write down a number in physics, you should h...

Metric Units and Conversions  What A unit is ais Unit conversion Conversion? a changing of one unit to another. Unit Examples:  meters  grams  inches  feet  pounds  seconds Any time you write down a number in physics, you should have a unit written after it!!!  What is a Metric Unit? Metric units are the universally excepted units around the world (except for the US). They are the easiest to convert. Metric Unit Examples: meters Base Units – all other liters metric units grams are based off of these (km, cm, ml, kg)  Dimensional Analysis CLE.3231.Math.1 Graph relationships and functions between manipulated (independent) variables and responding (dependent) variables.CLE.3231.Math.2 Solve for variables in an algebraic formula. Common Metric Units (Prefixes) Abbreviation Mega- M kilo- k hecto- h deka- da or D Base- m, l, g deci- d centi- c milli- m micro- µ nano- n  Metric Conversion Factors Knowing these conversion factors makes calculating conversions easy! 1 km= 1000 m These also work for liters 100 cm= 1 m and grams. Just replace the base unit (m) with a 1000 mm = 1 m (g) or (l). 10 mm = 1 cm Converting Units of Measurement Conversion factors are built from an equivalence statement which shows the relationship between the units in different systems.  Dimensional Analysis A mathematical way to convert one unit to another. This works for metric units and non- metric (English) units. This works by taking the unit you are given and multiplying it by a conversion factor. Converting Units of Measure 2.85 cm = ? in. 2.85 cm  conversion factor = ? in. Equivalence statement 2.54 cm = 1 in. Possible conversion factors Does this answer make sense?  Example 1: Convert 3m to cm For meters to cancel out, 3m 100 cm meters in the conversion 1m factor must be on the opposite side of the fraction (fence). Given Conversion Factor Multiply every number on top = 300cm of the fence and divide by the bottom. Example 2: Convert 1516 g to kg 1516 g 1 kg 1000 g conversion factor  1.516 kg  Problem 1 Convert 1200 cm to m.  Problem 2 Convert 5200 mL to L. Example 3: Convert 7200mm to km 7200 mm 1 cm 1 km 10 mm 100,000 cm =.0072 km  Problem 3 Convert 3 m to mm.  Non-Metric (English) Unit Conversions Common Conversion Factors 5280 ft = 1 mile 12 in = 1 ft 1 mile = 1600 m English to Metric 1 in = 2.54 cm conversion factors 3 ft = 1 yard Example 4: Convert 2 miles to ft 2 mi 5280 ft 1 mi = 10,560 ft  Problem 4 Convert 3.2 ft to inches. CLE.3231.Math.1 Graph relationships and functions between manipulated (independent) variables and responding (dependent) variables.CLE.3231.Math.2 Solve for variables in an algebraic formula.  Example 5: Convert 5 ft to cm 5 ft 12 in 2.54 cm 1 ft 1 in = 152. 4 cm  Problem 5 Convert 50 inches to m.  Example #1 A golfer putted a golf ball 6.8 ft across a green. How many inches does this represent? To convert from one unit to another, use the equivalence statement that relates the two units. 1 ft = 12 in 1 ft 12 in and The two conversion factors are: 12 in 1 ft  Example #1 A golfer putted a golf ball 6.8 ft across a green. How many inches does this represent? Derive the appropriate conversion factor by looking at the direction of the required change (to cancel the unwanted units). 12 in 6.8 ft ´ = in 1 ft  Example #1 A golfer putted a golf ball 6.8 ft across a green. How many inches does this represent? Multiply the quantity to be converted by the conversion factor to give the quantity with the desired units. 12 in 6.8 ft ´ = 82 in 1 ft  Example #2 An iron sample has a mass of 4.50 lbs. What is the mass of this sample in grams? (1 kg = 2.2046 lbs; 1 kg = 1000 g) 1 kg 1000 g 4.50 lbs ´ ´ = 2.04 ´103 g 2.2046 lbs 1 kg  B. Temperature Conversions There are three commonly used temperature scales, Fahrenheit, Celsius and Kelvin.  B. Temperature Conversions Converting between the Kelvin and Celsius Scales Note that  The temperature unit is the same size.  The zero points are different. To convert from Celsius to Kelvin, we need to adjust for the difference in zero points. TK = To C + 273  B. Temperature Conversions Converting between the Kelvin and Celsius Scales 70.o C = ? K To C + 273 = TK 70. + 273 = 343 K  B. Temperature Conversions Converting between the Fahrenheit and Celsius Scales Note  The different size units  The zero points are different To convert between Fahrenheit and Celsius, we need to make 2 adjustments. or 9o F ( ) To F = o To C + 32 5 C  Exercise At what temperature does C = F?  Solution Since °C equals °F, they both should be the same value (designated as variable x). Use one of the conversion equations such as: 5C ( TC = TF - 32 F   9F ) Substitute in the value of x for both TC and TF. Solve for x.  Solution 5C ( TC = TF - 32 F  9F  ) 5C ( x = x - 32 F   9F ) x = - 40 So - 40° C = - 40° F  C. Density Density is the amount of matter present in a given volume of substance. Common units are g/cm 3 or g/mL. C. Density  Example #1 A certain mineral has a mass of 17.8 g and a volume of 2.35 cm3. What is the density of this mineral? mass Density = volume 17.8 g Density = 2.35 cm3 3 Density = 7.57 g/cm  Example #2 What is the mass of a 49.6-mL sample of a liquid, which has a density of 0.85 g/mL? mass Density = volume x 0.85 g/mL = 49.6 mL mass = x = 42 g  Warm-Up Solve using Dimensional Analysis 1. Convert 45 inches to cm. 2. Convert 8 m to inches.  Warm-Up Using Dimensional Analysis 1. Convert 10ft to cm. 2. Convert 5 km to in. 3. 40 km/h to m/s 4. 200 °F to ° C 5. 500 K to ° C 6. Find ° C = °F