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SI Unit Conversions

When scientists finish an experiment, they often share their data with other scientists. To make sharing information easier, most of the world uses the SI system of measurement. SI, which stands for Systeme Internationale d’Unites, is a standard for measuring mass, length, volume, and other quantities. It is used by all scientists to avoid the confusion of comparing data that is based on different measuring systems. Three common SI units are shown in the chart on the right. Obviously, these three units are not suitable for all measuring needs. But, most of the quantities can be measured using one of these units with one of the prefixes in the chart.

Procedure: Converting between SI units is rather easy after you know the steps. To convert from one SI unit to another:

  1. Write the SI prefixes across your paper.
  1. Find the prefix that is given in the problem.
  2. Move across the chart to the new prefix.
  3. Move the decimal the same number of times and in the same direction as you did on the SI prefix chart.
  4. Re-write your final answers, including the appropriate units. 

Sample Problem One

Convert 500 decimeters (dm) into kilometers (km).

Step 1: Write out the SI prefixes.

        k        h        da        BASE                d        c        m

Step 2: Find the prefix given in the problem and circle it (we need to change 500 decimeters (dm), so the given prefix would be “d”).

        k        h        da        BASE                d        c        m

Step 3: Move across the chart to the new prefix (we are trying to find kilometers, so the new prefix would be “k”).

        k        h        da        BASE                d        c        m

Step 4: Now, move the decimal the same number of times and in the same direction as you did on the SI prefix chart. We had to move four places to the left. So, you need to move your decimal four places to the left

        700 dm         →                  700.0 dm         =          0.07 km

Sample Problem Two

How many milliliters (mL) are in 4.5 centiliters (cL)?

Step 1: Write out the SI prefixes.

        k        h        da        BASE                d        c        m

Step 2: Find the prefix given in the problem (we need to change 4.5 centiliters (cL), so the given prefix would be “c”).

        k        h        da        BASE                d        c        m

Step 3: Move across the chart to the new prefix (we are trying to find milliliters (mL), so the new prefix would be “m”).

        k        h        da        BASE                d        c        m

Step 4: Now, move the decimal the same number of times and in the same direction as you did on the SI prefix chart. We had to move one place to the right. So, you need to move your decimal one place to the right.

        4.5 cL          →          4.5 cL         =         45 mL

Practice Problems

Now, it’s your turn practice on your own. Remember, go step by step to solve each problem. Show your work – write out the prefix chart for each problem. Include units and circle your final answer.

  1. Covert 18 hg to kg.

  1. How many millimeters (mm) are in 46 centimeters (cm)?

  1. 0.9 deciliters (dL) is how many centiliters (cL)?

  1. Convert 4.9 grams to decagrams (dag).

  1. 146 centimeters (cm) is equal to how many meters (m)?

  1. Convert 3 centiliters (cL) to kiloliters (kL).

  1. How many millimeters (mm) are in 118 centimeters (cm)?

  1. How many decameters (dam) are in 36 meters (m)?

  1. Convert 82.29 hectometers (hm) into millimeters (mm).

  1. How many decimeters (dm) are in 64 kilometers (km)?

For the following problems, you do not have to write out the prefix chart, simply fill in the missing numbers and units in the problems below.

Creative Commons LicenseSI Unit Conversions by MN Partnership for Collaborative Curriculum is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.