Lesson 2: Converting Between SI Units - Move the Decimal Point

   Constructing Knowledge

Since SI units are related by powers of 10, you can convert between SI units by either multiplying by 10 or dividing by 10 the appropriate number of times. Conveniently, multiplying or dividing by 10 just changes the position of the decimal point. This means you can convert between SI units by just moving the decimal point!

You can use the Conversion Factor column in the SI Prefix Table to determine the direction and number of places to move the decimal point.

Prefix Conversion Factor Length Volume Mass
kilo 0.001 kilometre (km) kilolitre (kL) kilogram (kg)
hecto 0.01 hectometre (hm) hectolitre (hL) hectogram (hg)
deca 0.1 decametre (dam) decalitre (daL) decagram (dag)
Base Unit 1 metre (m) litre (L) gram (g)
deci 10 decimetre (dm) decilitre (dL) decigram (dg)
centi 100 centimetre (cm) centilitre (cL) centigram (cg)
milli 1000 millimetre (mm) millilitre (mL) milligram (mg)

To convert from one SI unit to another, using the strategy of moving the decimal, follow the steps below.

  1. Using the SI Prefix table, write the conversion ratio as an equality, and determine in which direction the decimal moves and how many places it moves.

  2. Repeat the same decimal movement (direction and number of places) to the measurement given.

A general rule is that when you are moving to a unit that is higher on the chart, the decimal will move to the left. When you are moving to a unit lower on the chart, the decimal will move to the right.

   Multimedia

A video demonstrating converting units by moving the decimal point is provided.


EXAMPLE 1

Convert 450 milligrams to decagrams, using the decimal point strategy.

Solution


Step 1: Using the SI Prefix table, write the conversion ratio as an equality, and determine in which direction the decimal moves and how many places it moves.

1000 mg = 0.1 dag. To convert from mg to dag move the decimal point 4 places to the left.



Remember that if a decimal is not shown, it is at the right end of the number.
1000 = 1000.

Step 2: Repeat the same decimal movement (direction and number of places) to the measurement given.

Now repeat this same movement with the given value.



As you can see, we inserted a 0 into the space in front of 4 so the decimal can be placed one digit away from the 4.


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