The ladder method is a simple way of performing metric conversions using conversion factors. There are two ways of using the method. The first is moving the decimal point in a number to the left or right. The second is canceling out units in a ladder or chain.
Defining a Unit
When defining a unit, you first define a means of measuring that physical quantity. Measuring, in turn, is a method of calculating the quantity from other known quantities. Science today uses an international system of units known as SI units. (SI comes from the French “Système International d’unités”). Each prefix in the SI system is 10 units apart, meaning you can perform conversions just by moving the decimal point.
While SI is the standard for most cases, occasionally other systems are used. The old Imperial system is still in use in the United States for many common day to day uses. The metric system was the precursor to the modern SI system but has some minor differences.
Moving the Decimal Point in the Ladder Method
Using the ladder method for metric conversions is as easy as moving the decimal point.
- Move the decimal point to the right when converting from larger to smaller units
Example: 4.2 km = 4200 m - Move the decimal point to the left when converting from smaller to larger units
Example: 0.0025 mg = 2.5 g
A simple mnemonic device for remembering the main metric prefixes is:
King Henry Died Drinking Chocolate Milk
(kilo hecta deca deci centi milli)
Using the Ladder Method in Calculation
The Background
One common procedure is converting a measurement between measuring systems using conversion factors. An example of a conversion factor is
1 km = 1000 m
There are 1000 meters in 1 kilometer. If you want to know how many meters are in 3 kilometers, you use this conversion factor to calculate the result.
This is possible because you are just multiplying the measurement by 1. This can be seen by dividing both sides of the conversion factor equation by one of the units.
Divide both sides of the conversion factor by 1 km
The same is true if you divide both sides by 1000 m
It doesn’t change the value of the measurement when you multiply by the conversion factor. It just changes the units the measurement is compared to. This method of unit conversion is called “Unit Cancelling” because the undesired unit is canceled out by the conversion factor.
Take the 3 kilometer example above. The kilometer unit is canceled out leaving only meters on both sides of the equation.
The Ladder Method
Occasionally you perform multiple conversions in a row to get the units you need on a measurement. Since all you are doing is multiplying the base measurement by 1, you can perform all of the conversions as one long chain of conversion factors. This method is known as the “Ladder Method”. Each conversion step is another rung of a ladder to cancel out the undesired units.
For example, if you convert 18 km/hr to m/s, you use the following conversion factors:
1000 m = 1 km
60 min = 1 hr
60 s = 1 min
The goal in this conversion is ending up with meters in the numerator and seconds in the denominator. Set up your conversions so the undesired units are canceled out.
If you go ahead and perform the final calculation, the above equation reduces to:
So, 18 km/hr = 5 m/s.