1. UNIT CONVERSIONS

2. Why is it necessary to understand how to convert between systems of units?

3. UNIT CONVERSIONS Why is it necessary to understand how to convert between systems of units? Unfortunately many methods or units were created for measuring the same thing.

4. UNIT CONVERSIONS Why is it necessary to understand how to convert between systems of units? Unfortunately many methods or units were created for measuring the same thing. To understand the value of a number it must be in a unit easily understood.

5. UNIT CONVERSIONS EXAMPLE: World currencies. Most countries have their own unit of monetary value.

6. UNIT CONVERSIONS The number on the bill might make you think a bill is very valuable.

7. UNIT CONVERSIONS But the real value becomes apparent when attempting to purchase something.

8. UNIT CONVERSIONS But the real value becomes apparent when attempting to purchase something. This boy has only a few dollars worth of the Zimbabwe Dollar (2008) The Zimbabwe dollar must not be worth much.

9. UNIT CONVERSIONS In fact the Zimbabwe Dollar has become so low in value that people have actually tossed them in the trash bin. one $200 000 = $0.0002 US dollars!

10. UNIT CONVERSIONS There have been many cases of drastic drops in value of currency. Here a street sweeper is cleaning up discarded money.

11. UNIT CONVERSIONS The value in dollars is important because it is in a unit you understand or are used to using.

12. UNIT CONVERSIONS Of course the value of the dollar can fluctuate, which is different from most things where conversions are necessary.

13. UNIT CONVERSIONS The equivalence or exchange rate is also known as the CONVERSION FACTOR. 1 = $3.67 ( August 2011)

14. UNIT CONVERSIONS Most conversion factors do not change. They are listed in tables. It is important to be able to work from these tables. These tables will always be provided. Length 1 meter = 100 cm 1 meter = 1000mm 1 meter = 3.281 feet 1 inch = 2.54 centimeters 1 foot = 12 inches 1 foot = 0.308 meters 1 mile = 5280 feet 1 mile = 1.6 kilometers Volume 1 liter = 1000 cm 3 1 liter =.001 m 3 1 liter = 0.0351 ft 3 1 cm 3 = 1cc 1 ft 3 = 0.02832 m 3 1 ft 3 = 28.32 liters 1 ft 3 = 7.477 gallons Mass 1 slug = 14.6 kilograms 1 kilogram = 1000grams Time 1 minute = 60 seconds 1 hour = 60 minutes 1 day = 24 hours 1 year = 365 days (roughly)

15. UNIT CONVERSIONS Unit conversions are based on the Identity Property of Multiplication. Simply Stated: The product of any number and 1 will be the number you started with.

16. UNIT CONVERSIONS Unit conversions are based on the Identity Property of Multiplication. Simply Stated: The product of any number and 1 will be the number you started with. Mathematically: Z × 1 = Z

17. UNIT CONVERSIONS Unit conversions are based on the Identity Property of Multiplication. Simply Stated: The product of any number and 1 will be the number you started with. Mathematically: Z × 1 = Z or ☺ × 1 = ☺ or ♣ × 1 = ♣

18. UNIT CONVERSIONS So, as long as a number (X) is multiplied by 1 the product will be the value (X).

19. UNIT CONVERSIONS So, as long as a number (X) is multiplied by 1 the product will be the value (X). EXAMPLE:

20. UNIT CONVERSIONS So, as long as a number (X) is multiplied by 1 the product will be the value (X). EXAMPLE: Here the ratio has the value of one.

21. UNIT CONVERSIONS When units of measure are included a ratio may appear that it is not equal to one but it is when the units are taken into account. EXAMPLE:

22. UNIT CONVERSIONS When units of measure are included a ratio may appear that it is not equal to one but it actually is when the units are taken into account. EXAMPLE: Because 12 inches equals 1 foot the ratio: has a value of 1

23. UNIT CONVERSIONS When units of measure are included a ratio may appear that it is not equal to one but it actually is when the units are taken into account. EXAMPLE: Because 12 inches equals 1 foot the ratio: has a value of 1 Numerator & Denominator have the same value

24. UNIT CONVERSIONS Let’s see how a simple conversion factor is used. EXAMPLE: How many inches are in 3.5 feet?

25. UNIT CONVERSIONS Let’s see how a simple conversion factor is used. EXAMPLE: How many inches are in 3.5 feet? Start by writing the number given in the question over one with the units.

26. UNIT CONVERSIONS Let’s see how a simple conversion factor is used. EXAMPLE: How many inches are in 3.5 feet? Start by writing the number given in the question with the units

27. UNIT CONVERSIONS Let’s see how a simple conversion factor is used. EXAMPLE: How many inches are in 3.5 feet? Then multiply by a ratio and show where your solution will be.

28. UNIT CONVERSIONS Let’s see how a simple conversion factor is used. EXAMPLE: How many inches are in 3.5 feet? Write in the units you want to get to in the solution.

29. UNIT CONVERSIONS Let’s see how a simple conversion factor is used. EXAMPLE: How many inches are in 3.5 feet? Write in the units you want to get to in the solution. These units will also go in the numerator of your conversion factor. This way the unit of inches comes out in the solution.

30. UNIT CONVERSIONS Let’s see how a simple conversion factor is used. EXAMPLE: How many inches are in 3.5 feet? Now write in the unit you are converting from in the denominator. This will make it cancel out when the values are multiplied together.

31. UNIT CONVERSIONS Let’s see how a simple conversion factor is used. EXAMPLE: How many inches are in 3.5 feet? Notice the feet will cancel leaving only the unit of inches.

32. UNIT CONVERSIONS Let’s see how a simple conversion factor is used. EXAMPLE: How many inches are in 3.5 feet? Units cancel like numbers.

33. UNIT CONVERSIONS Let’s see how a simple conversion factor is used. EXAMPLE: How many inches are in 3.5 feet? Now put in the numbers for the conversion factor 1 foot = 12 inches.

34. UNIT CONVERSIONS Let’s see how a simple conversion factor is used. EXAMPLE: How many inches are in 3.5 feet? To complete the work numbers in the numerator (top) are multiplied and numbers in the denominator (bottom) are divided. Units are cancelled where they can be.

35. UNIT CONVERSIONS Let’s see how a simple conversion factor is used. EXAMPLE: How many inches are in 3.5 feet? Yes, this ends up simply being 3.5 x 12 but it is important to understand how the units work on a simple problem so that you can apply the same idea to more complicated problems.

36. UNIT CONVERSIONS Let’s try another simple example. EXAMPLE: A sign states 150 kilometers to Boston. How many miles is this? Write the number with units over 1 multiplied by a ratio equal to the units your trying to get to.

37. UNIT CONVERSIONS Let’s try another simple example. EXAMPLE: A sign states 150 kilometers to Boston. How many miles is this? Put the units you are attempting to get to in the numerator of the ratio. Also put the units you are trying to cancel in the denominator.

38. UNIT CONVERSIONS Let’s try another simple example. EXAMPLE: A sign states 150 kilometers to Boston. How many miles is this? Put the appropriate numbers in the conversion factor ratio

39. UNIT CONVERSIONS Let’s try another simple example. EXAMPLE: A sign states 150 kilometers to Boston. How many miles is this? Put the appropriate numbers in the conversion factor ratio

40. UNIT CONVERSIONS Let’s try another simple example. EXAMPLE: A sign states 150 kilometers to Boston. How many miles is this? Cancel units where possible.

41. UNIT CONVERSIONS Let’s try another simple example. EXAMPLE: A sign states 150 kilometers to Boston. How many miles is this? Now you have division 150 / 1.6 = 93.75 Remember, numbers in the top are multiplied and numbers in the bottom are divided.

42. UNIT CONVERSIONS Let’s try a conversion where the unit is more complex. EXAMPLE: A bullet travels at 800 feet/second, how many miles/hour is this? Now

43. UNIT CONVERSIONS Let’s try a conversion where the unit is more complex. EXAMPLE: A bullet travels at 800 feet/second, how many miles/hour is this? This conversion includes a unit in the numerator and denominator. This will require more than a single conversion factor.

44. UNIT CONVERSIONS Let’s try a conversion where the unit is more complex. EXAMPLE: A bullet travels at 800 feet/second, how many miles/hour is this? Write the number given in the question with the feet in the numerator and the seconds in the denominator.

45. UNIT CONVERSIONS Let’s try a conversion where the unit is more complex. EXAMPLE: A bullet travels at 800 feet/second, how many miles/hour is this? Multiply by two ratios and make it equal to the desired units.

46. UNIT CONVERSIONS Let’s try a conversion where the unit is more complex. EXAMPLE: A bullet travels at 800 feet/second, how many miles/hour is this? Put the desired units into the ratios.

47. UNIT CONVERSIONS Let’s try a conversion where the unit is more complex. EXAMPLE: A bullet travels at 800 feet/second, how many miles/hour is this? Put the units you are converting from into the ratios.

48. UNIT CONVERSIONS Let’s try a conversion where the unit is more complex. EXAMPLE: A bullet travels at 800 feet/second, how many miles/hour is this? Notice how the units will cancel.

49. UNIT CONVERSIONS Let’s try a conversion where the unit is more complex. EXAMPLE: A bullet travels at 800 feet/second, how many miles/hour is this? Now write in the numbers for the conversion factors.

50. UNIT CONVERSIONS Let’s try a conversion where the unit is more complex. EXAMPLE: A bullet travels at 800 feet/second, how many miles/hour is this? Now write in the numbers for the conversion factors.

51. UNIT CONVERSIONS Let’s try a conversion where the unit is more complex. EXAMPLE: A bullet travels at 800 feet/second, how many miles/hour is this? Complete the math: 800 ÷ 5280 x 3600 = 545