The example in the previous section is a real world application of dimensional analysis. Dimensional analysis is used in science quite often. In this section, you will look at common unit conversions used in science.

The STAAR reference materials for Chemistry and Physics both have a section titled Constants and Conversions. Refer to this during your STAAR Test.

Source: STARR Reference Material, Texas Education Agency

Listed below are some other common unit conversions as well as common metric prefixes used in science.

Let’s practice a few unit conversions using dimensional analysis. Remember the steps we learned in section 1.

  1. Write the given information as a fraction by placing it over 1. (Placing it over 1 makes it a fraction but does not change its value.)
  2. Write a conversion factor that has the unit you want to remove in the denominator and the unit you want to end up with in the numerator. After you fill in your units, add the numbers. (Usually one of the numbers is a 1, but it can be in either the denominator or the numerator.) Note: In some cases you may need to repeat this step a number of times in order to get the unit you want to end up with in the numerator.
  3. Mark through the units to double check that they all cancel and that you are left with the units you want.
  4. Multiply the numbers in the numerators, and then multiply the numbers in the denominators.
  5. Divide the numerator but the denominator. Be sure to add your units to your final answer.

Try these problems

  1. Determine the number of centimeters in 3.5 miles. Use the following conversion factors and use conversion factors that you already know to answer the question.

    1 mile = 5280 ft.         2.54 cm = 1 inch

    Interactive popup. Assistance may be required.

    Check Your Answer

    563270.4 cm
    Close Pop Up

  2. Determine the number of mm in 1.4 inches. Use the conversion factors from the tables above.

    Interactive popup. Assistance may be required.

    Check Your Answer

    35.56 mm
    Close Pop Up

  3. Convert 28316 cm3 to ft3. Use the conversion factors from the tables above.

    Interactive popup. Assistance may be required.

    Check Your Answer

    1 ft3
    Close Pop Up