Example

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The following example shows how to form a unit conversion.

Example.

12 in = 1 ft

Divide both sides by 1 ft.

[latex]\frac{12\;in}{1\;ft}=\frac{\cancel{1\;ft}}{\cancel{1\;ft}}[/latex]

[latex]\frac{12\;in}{1\;ft}=1[/latex]

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Example

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Consider the area of the rectangle below.

Area = (5 ft) (6 ft)

[latex]30\;ft^2[/latex]

To find the area in square inches, convert each side length to inches. Then multiply the results together.

[latex]\cancel{5\;ft}\cdot\frac{12\;in}{\cancel{1\;ft}}=\;60\;in[/latex]

[latex]\cancel{6\;ft}\cdot\frac{12\;in}{\cancel{1\;ft}}=\;72\;in[/latex]

Area = (60 in) (72 in)

4, 320 [latex]in^2[/latex]

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Convert.

1. 10 km = __________________ mi
2. 120 g = _________________ [latex]\mu g[/latex]
3. 2.40 mi = _______________ ft
4. [latex]17.0\;in^2=[/latex] _________________ [latex]cm^2[/latex]
5. 0.850 qt = _________________ mL
6. 61.0 cm = _____________ ft
7. 5L = ____________ pt
8. 10.0 in = _______________ cm
9. 320 oz = _______________ ib
10. 1 year = _______________ min
11. 120 m = _______________ yd
12. [latex]2.4\;mi^2\;=[/latex] _______________ [latex]ft^2[/latex]
13. 102 gal = _____________ [latex]in^3[/latex]
14. [latex]150\;m^3\;=[/latex] _________________ [latex]ft^3[/latex]
15. 1950 g = ________________ ib
16. 1.2 kg = ________________ oz
17. 2L = _________________ pt
18. 725 ft = _______________ m
19. 95 L = ________________ gal
20. 60 mph = ________________ m/s
21. [latex]5.93\;cm^3=[/latex] _______________ [latex]m^3[/latex]
22. [latex]1\;ft^3=[/latex] ____________________ [latex]m^3[/latex]
23. [latex]1.42\;g/cm^2\;=[/latex] __________________ [latex]mg/mm^2[/latex]
24. [latex]8.24\;g/cm^2=[/latex] ____________________ [latex]mg/mm^2[/latex]

Perform the following conversions to answer the following.

25. Convert 10,000 meters to miles two different ways.

26. When converting from [latex]ft^2[/latex] to [latex]mi^2[/latex], explain what it means to use the unit conversion twice.

27. Usain Bolt, the fastest recorded human, has been clocked at 12.43 meters per second. A student performs the following conversion into miles per hour (12.43)(0.3048)(5,280)(60)(60) = 72,014,925.3 mph

1. 1. Is this answer reasonable?
   2. Explain in your own words the errors made.
   3. What is the correct answer in miles per hour?

28. 130 meters per second into miles per hour

29. 1100 feet per second into miles per hour

30. 53 yards per hour into inches per week

31. 721 lb per week into kg per second

32. A regulation pitcher’s mound is [latex]10\frac12[/latex] inches off the ground. Which of the following would be an appropriate alternative unit of measurement for this distance?

1. 1. Centimeters
   2. Feet
   3. Kilometers
   4. Grams
   5. Miles

33. The distance from a Port Huron to the Indiana State line is approximately 281 miles (via I-94). Express this distance in kilometers.

34. A baby born in the US weighs 3.485 kg according to the scale in the birthing room. Convert this to pounds and ounces so you can tell the grandparents how much the baby weighed.

35. Nick Cave’s new movie is titled 20,000 Days on Earth. How old is Nick if the title was correct that he has been alive for 20,000 days (in years and months)?

36. How many years old are you if you have lived 1 billion seconds?

37. The length of a football field is 100 yards. Which of the following is an equivalent measurement? (More than one answer may be correct.)

1. 1. 300 feet
   2. 100 meters
   3. 9,144 centimeters
   4. 914.4 meters
   5. 10,000 centimeters

38. A gallon of chocolate milk sells for $3.14. A snack-size bottle of chocolate milk sells for 3 cents per ounce. Which is a more economical purchase? Show your work to explain why.

39. If you travel 65 mph, how many feet can you travel in 22 minutes?

40. A child requires a 4.5 mL dose of medicine each day. How many days would a cup of this medicine last?

41. San Antonio is 465 [latex]mi^2[/latex]. Houston is [latex]1,623.92\;km^2[/latex]. Which city is bigger and by how much?

42. Scientists estimate the total amount of fresh water on earth to be [latex]3.73\;\times\;10^8\;km^3[/latex]. What is this volume in cubic meters? In liters? [latex](1\;{\text{liter}}\;=\;0.001\;m^3)[/latex]

43. How many years old are you if you have lived 1 trillion seconds?

44. 1 mL of ink can print 50 pages of text. If you had 5 gallons of ink then how many pages could you print?

45. At his annual physical, Tony measured 6 feet, 2 inches tall. How many centimeters tall is he?

46. The pediatrician tells the parents that their child is 92 centimeters tall. How tall is the child in feet and inches?

47. A newborn baby is 53 centimeters long. How many inches long is she?

48. A patient weighs 56 pounds. How many kilograms does she weigh?

49. Last year Daniel donated 1892.72 milliliters of blood. If a person donates 1 pint each time, how many times did Daniel donate blood last year?

For the next two problems, use the dosage instructions in the following table.

Age (years)	Weight (lb)	Dose
Under 4	Under 36	Do not use
4–5	36–47	1 tsp
6–11	48–95	2 tsp
12–Adult	Over 95	1 Tbsp

50. If a child, age 4, weighs 36 pounds, how many milliliters of medicine will he take per dose?

51. If a child, age 12, weighs 105 pounds, how many milliliters of medicine will she take per dose?

52. Blood makes up 7% of a body’s weight. If a person weighs 175 lb, how much would his blood weigh? Provide the answer in both pounds and kilograms.

53. The average body has 10 pints of blood. How many ounces of blood are in a body?

54. Using your answer from 68, how many mL of blood are in the body?

55. How many [latex]cm^3[/latex] (cc) are in [latex]\frac12[/latex] tsp?

56. How many qt are in 4 fl oz?

57. Convert 0.05 g to [latex]\mu g[/latex]

58. Convert 0.0025 L to [latex]cm^3[/latex] (cc).

59. How many tsp are in 2 Tbsp?