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Dimensional Analysis

  • In order to perform dimensional analysis, choose a conversion factor that causes the units you have to cancel and the units you want to remain.
  • It is helpful to memorize these conversion factors.
  • Length
    12 in = 1 ft
    36 in = 1 yd
    3 ft = 1 yd
    5280 ft = 1 m
    Weight
    16 oz = 1 lb
    2000 lb = 1 t
    Capacity
    8 fl oz = 1 cup
    2 cups = 1 pt
    4 cups = 1 qt
    2 pt = 1 qt
    4 qt = 1 gal

Dimensional Analysis

Convert 2.4 miles into feet. Use the conversion factor [(5280 ft)/(1 mi)].

  • 2.4 mi ×[(5280 ft)/(1 mi)] =

12,572 ft

Convert 2[3/4] pounds to ounces. Use the conversion factor [(16 oz)/(1 lb)].

  • 2[3/4] lb ×[(16 oz)/(1 lb)] =
  • [11/4] lb ×[(16 oz)/(1 lb)] =
  • [11/1] lb ×[(4 oz)/(1 lb)] =

44 oz

Convert 7.2 cups to fl oz. Use the conversion factor [(8 fl oz)/(1 cup)].

  • 7.2 cups ×[(8 fl oz)/(1 cup)] =

57.6 fl oz

Convert 13,400 lb to tons. Use the conversion factor [(2000 lb)/(1 t)].

  • 13,400 lb ×[(1 t)/(2000 lb)] =

6.7 t

Find the unit rate for traveling 3,500 miles in 22.5 minutes.

  • [(3,500 mi)/(22.5 min)] = [?/(1  min)]
  • [(3,500 ÷22.5)/(22.5 ÷22.5)] = [?/1]

[(155.56 mi)/(1 min)]

A group project will require 30 hours of total work in order to be completed. If there are 5 people in the group working on the project at the same time, how long will the project take?

  • [(30 hours)/(5 people)] =

6 hours

A scale needs 6 pounds on one side to balance out the other. How many 12-ounce weights will you need to balance the scale?

  • 6 lb ×[(16 oz)/(1 lb)] = 96 oz
  • 96 oz ÷ 12 oz =

8 weights

A quilt needs to be 6 feet long. How many 4-inch blocks of cloth will you need, length-wise, to make the quilt?

  • 6 ft ×[(12 in)/(1 ft)] = 72 in
  • 72 in ÷ 4 in =

18 blocks of cloth

[(15 gal)/(1 min)] = ?[pt/s]

  • 2 pt = 1 qt
  • 4 qt = 1 gal
  • 1 min = 60 s
  • [(15 gal)/(1 min)] ×[(4 qt)/(1 gal)] ×[(2 pt)/(1 qt)] ×[(1 min)/(60 s)] =
  • [(120 pt)/(60 s)] =

[(2 pt)/s]

[(780 in)/(5 s)] = ?[m/days]

  • 12 in = 1 ft
    5280 ft = 1 m
    60 s = 1 min
    60 min = 1 hr
    24 hr = 1 day
  • [(780  in)/(5 s)] ×[(1 ft)/(12 in)] ×[(1 mi)/(5280 ft)] ×[(60 sec)/(1 min)] ×[(60 min)/(1 hr)] ×[(24 hr)/(1  day)] =
  • [(67,392,000 m)/(316,800 days)] =

[(212.72 m)/day]

*These practice questions are only helpful when you work on them offline on a piece of paper and then use the solution steps function to check your answer.

Answer

Dimensional Analysis

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Mathematics: Pre Algebra