A DIMENSIONAL ANALYSIS “HOW TO”

Dimensional analysis is a way of making conversions and solving problems using equivalent units. In this process, we use conversion factors that equal 1.

Directions:

  • Put the GIVEN unit on the top left. If it is a single unit (cm) put a 1 as the denominator on the bottom. If it is a derived unit (g/cm3), put the denominator unit on the bottom.
  • Next, use conversion factors (statements equal to 1) that link your given to what you need to find. Sometimes it will take more than one step.
  • Write your conversion factor so that its units will cancel with the previous unit (diagonal to the same unit before it).
  • If the given is a derived unit you may need more than one conversion factor. For example, if you are converting mi/hr to km/sec you need to convert miles to kilometers and hours to seconds. It doesn’t matter which you do first.
  • Before doing the math, cancel all units that you can cancel. You should be left with the unit(s) you are trying to find. If your conversion factors are correct and you put numbers in the calculator correctly, you will get the correct answer. If you do not end up with the correct units, the set-up is incorrect.

DO THESE PROBLEMS USING DIMENSIONAL ANALYSIS:

You must show all steps as shown below.

  1. 186,000 m sec min = m/hr

1 sec min hr

  1. How many milliliters of water will it take to fill a 2 liter bottle that already contains 1.87 L of water?
  1. The speed of sound under normal condition is approximately 1,100 feet per second. How many miles per hour is this? (1 mile = 5,280 feet)
  1. An automobile uses 0.05 mL of oil for each kilometer it is driven. How much oil in liters is consumed if the automobile is driven 20,000 km?
  1. At the equator, Earth rotates with a velocity of about 465 m/s.

a)What is this velocity in kilometers per hour?

b)What is this velocity in kilometers per day?

6. Make the following conversions:

a) 147 grams to kilograms

b) 245,000 mL to kiloliters

c) .0059 km to centimeters

d) 34,981 micrograms to grams

e) 3.72 L/hr to cubic centimeters per minute

f) 6.12 km/hr to meters per second

7. Percent error is defined as the difference between the experimental value and the accepted value dived by the accepted value.

% error = experimental – accepted /accepted

Multiply your answer by 100 to make it a percent.

a)A student estimated the volume of water in a beaker as 150. mL. When she poured the water into a graduated cylinder it measured 158 mL. What is the percent error?

b)In lab Mary measured the boiling point to be 99.1oC. She knew that the accepted boiling point for water is 100.oC. What was her percent error?

c)During Chemistry, Jim found the density of his unknown metal to be 2.56 g/cm3. His teacher told him afterwards that his metal was aluminum which has a density of 2.70 g/cm3. What was his percent error?