1 / 14

Dimensional Analysis (Factor-Label Method)

How can we convert units?. Dimensional Analysis (Factor-Label Method). Every measurement needs to have a value ( number ) and a unit ( label ). Without units, we have no way of knowing what the actual measurement is

constance
Télécharger la présentation

Dimensional Analysis (Factor-Label Method)

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. How can we convert units? Dimensional Analysis(Factor-Label Method)

  2. Every measurement needs to have a value (number) and a unit (label). • Without units, we have no way of knowing what the actual measurement is • Sometimes the units that something is measured in, need to be converted into a comparable unit for a calculation • So how do we convert our units into new units? Measurements

  3. When we are converting from one metric unit to another, all we need to do it move the decimal point • Convert the following: k h da _ d c m • 15.6 dm = _________ hm • 3.0 s = _________ ms • 254 g = _________ kg Metric Conversions Review 0.0156 3000 0.254

  4. Not every type of conversion that you will encounter will be a metric conversion where you can just move the decimal Dimensional Analysis (Factor-Label Method) is the process that we can use to mathematically convert units from one unit system to another Other Conversions

  5. Before we can look at examples of dimensional analysis, let’s review some basic math principles: • What happens when you divide a number by itself? • What happens when you divide a unit by itself? • In both cases, you get the number 1. • Dimensional analysis involves multiplication and division using conversion factors. • Conversion factors : two numbers with their units that are equivalent to each other • i.e. 1 foot = 12 inches, 12 eggs = 1 dozen Getting Started

  6. Conversion Factors • Conversion factors can be written as ratios because both values equal each other • Because they equal each other, if we divide the quantities they would be equal to one. • For Example: 12 inches = 1 foot • Written as an “equality” or “ratio” it looks like: or = 1 = 1 • When a value is multiplied by a conversion factor the units behave like numbers do when you multiply fractions: If you have the same units in both the numerator and the denominator, they cancel!

  7. Example Problem #1 • How many feet are in 60 inches? • Solve using dimensional analysis. • All dimensional analysis problems are set up the same way. They follow this same pattern: What units you have x What units you want = What units you want What units you have The number & units you start with The units you want to end with The conversion factor (The equality that looks like a fraction)

  8. Example Problem #1 (cont) • You need a conversion factor. Something that will change inches into feet: 12 inches = 1 foot • Write this conversion factor as a ratio, making sure that the number on the bottom of the ratio has units that match the units of your starting units so that they will cancel 60 inches x 5 feet = • Do the math: • 1. Multiply all of the numerators first: 60 x 1 = 60 • 2. Multiply all of the denominators: 12 x 1 = 12 • 3. Divide the product of the numerators by the product of the denominators: 60 ÷ 12 = 5

  9. Example Problem #1 (cont) • The previous problem can also be written to look like this: • 60 inches 1 foot = 5 feet • 12 inches • Using this format, the vertical lines mean “multiply” and the horizontal bars mean “divide.”

  10. Let’s practice setting up dimensional analysis problems using nonsense units: 1. How many bleeps are in 12 cams? 2. How many nerds are in 6 tongs? 3. How many yips are in 15 cams? (Hint: Use 2 conversion factors!) Conversion Practice 1 Conversion Factors: 3 bops = 5 yips 20 nerds = 8 cams 2 cams = 1 bleep 2 nerds = 3 tongs 1 bop = 5 cams 12 cams x1 bleep 2 cams = 6 cams 6 tongs x2 nerds 3 tongs = 4 nerds 15 cams x1 bop 5 cams x 5 yips 3 bops = 5 yips

  11. Common Conversion Factors Units of Length12 inches = 1 foot 3 feet = 1 yard 5280 feet = 1 mile 1 inch = 2.54 centimeters 1 foot = 0.305 meters 1 mile = 1.609 kilometers 1 mile = 1609 meters Units of Time 1 hour = 60 minutes 1 minute = 60 seconds 1 hour = 3600 seconds Units of Volume 2 cups = 1 pint 2 pints = 1 quart 4 quarts = 1 gallon 16 fluid ounces = 1 pint 1 gallon = 3.79 liters 1 fluid ounce = 29.6 milliliters Units of Mass16 ounces = 1 pound 2000 pounds = 1 ton 1 ounce = 28.35 grams 1 pound = 0.454 kilograms

  12. 22.1 cm ______ 1 in 2.54 cm ________ 2.54 cm 1 in ______ ( ) 2.54 cm 1 in Now let’s practice conversions with real units: 1. How many centimeters is 8.72 in? Conversion Practice 2 equality: 2.54 cm = 1 in applicable conversion factors: or 8.72 in x = Again, the units must cancel.

  13. 1 ft ______ 1 ft 12 in 12 in ( ) ______ 12 in ____ 1 ft 3.28 ft equality: 1 ft = 12 in 2. How many feet is 39.37 inches? applicable conversion factors: or 39.37 in x = Again, the units must cancel.

  14. equalities: 1 mile = 1609 meters 3600 s = 1 hour 3. Convert 65 meters/second into miles per hour. (2 part units!) 1. Convert your distance from meters to miles: 2. Convert your seconds into hours: 3. Divide your miles by hours: 65 meters x1 mile 1609meters = 0.0404 miles 1 second x1 hour 3600 seconds = 0.000278 hrs 0.0404 miles 0.000278 hrs. = 145 mi/hr

More Related