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Dimensional Analysis
(Speech to Middle High School Students)
How many of you could figure out as quickly as is possible, the number of seconds which are
in one day? I will give you about one minute to try to get the answer and you may use your
calculators. If you tried to work out the answer, but got confused by the process, I want to show
you a method which I believe will help you very well. So let’s begin. Some of you might have
found it confusing to do the conversion, because you have to go from day to hours, hours to
minutes and minutes to seconds. To do this quickly and with little or no error, we will use a
method which is simple and organized. We know that 60 seconds give us one minute, 60 minutes
give one hour, and 24 hours give one day. Using our method, this is what we will have:
You will notice that we cancel the same units between top and bottom and the remaining units
and values give us our answer. That is, we cancel the top and bottom “minute” units and also the
top and bottom “hour” units. Our cancellation leaves us with the “second” unit at the top, and
“day” unit at the bottom with the corresponding values. After multiplying the top numbers
together and the bottom numbers together, we get a final answer of 86,400 seconds in I day.
The method we have just employed is called dimensional analysis. This method which is also
known as the factor-label method, unit-factor method or unit-analysis method, “ is a problem-
solving method that uses the fact that any number or expression can be multiplied by 1 without
changing its value,” (Math skills review dimensional analysis). In other words, Dimensional
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analysis is a method in which conversions are done between quantities, with the units of
measurements playing a key role in the conversion processes. In other methods of conversions,
units do not play a key role. They simply help to determine the conversion factor, but are not a
part of the calculation process. However, in dimensional analysis, units are cancelled, leaving the
values to give us the final answer, as well as the units related to the answer. To put it simply, this
method allows us to do conversions between measurements, with the units being used in the
cancellation process.
So how does dimensional analysis work? Well, one thing to note is that the method makes
use of a conversion factor or multiplier, which is always equal to 1. This factor is a number
which is written as a fraction or ratio, and is used to change measurements from one unit to
another. We must remember that in this matter of conversions, all data must be based on the
same item. For example, if we are dealing with time, all data must be related to time, and if we
are dealing with distance, all data must be distance related, and so on. Dimensional analysis has a
wide range of application, from simple basic math to very advanced areas of problem solving,
and it is used in numerous fields such as engineering, medicine, business and education. The
truth is, this method is very versatile, and anyone can learn to use it, and apply it to any field of
work. For example, you are organizing a party for someone and donuts will be served among
other things. You know that 40 persons will be attending the party, and each box contains 6
donuts. How many boxes must you order if each person eats 3 donuts? You need to figure this
out quickly. Well, the best thing to do is to apply dimensional analysis like this:
Dimensional Analysis
(Speech to Middle High School Students)
How many of you could figure out as quickly as is possible, the number of seconds which are
in one day? I will give you about one minute to try to get the answer and you may use your
calculators. If you tried to work out the answer, but got confused by the process, I want to show
you a method which I believe will help you very well. So let’s begin. Some of you might have
found it confusing to do the conversion, because you have to go from day to hours, hours to
minutes and minutes to seconds. To do this quickly and with little or no error, we will use a
method which is simple and organized. We know that 60 seconds give us one minute, 60 minutes
give one hour, and 24 hours give one day. Using our method, this is what we will have:
You will notice that we cancel the same units between top and bottom and the remaining units
and values give us our answer. That is, we cancel the top and bottom “minute” units and also the
top and bottom “hour” units. Our cancellation leaves us with the “second” unit at the top, and
“day” unit at the bottom with the corresponding values. After multiplying the top numbers
together and the bottom numbers together, we get a final answer of 86,400 seconds in I day.
The method we have just employed is called dimensional analysis. This method which is also
known as the factor-label method, unit-factor method or unit-analysis method, “ is a problem-
solving method that uses the fact that any number or expression can be multiplied by 1 without
changing its value,” (Math skills review dimensional analysis). In other words, Dimensional
, 2
analysis is a method in which conversions are done between quantities, with the units of
measurements playing a key role in the conversion processes. In other methods of conversions,
units do not play a key role. They simply help to determine the conversion factor, but are not a
part of the calculation process. However, in dimensional analysis, units are cancelled, leaving the
values to give us the final answer, as well as the units related to the answer. To put it simply, this
method allows us to do conversions between measurements, with the units being used in the
cancellation process.
So how does dimensional analysis work? Well, one thing to note is that the method makes
use of a conversion factor or multiplier, which is always equal to 1. This factor is a number
which is written as a fraction or ratio, and is used to change measurements from one unit to
another. We must remember that in this matter of conversions, all data must be based on the
same item. For example, if we are dealing with time, all data must be related to time, and if we
are dealing with distance, all data must be distance related, and so on. Dimensional analysis has a
wide range of application, from simple basic math to very advanced areas of problem solving,
and it is used in numerous fields such as engineering, medicine, business and education. The
truth is, this method is very versatile, and anyone can learn to use it, and apply it to any field of
work. For example, you are organizing a party for someone and donuts will be served among
other things. You know that 40 persons will be attending the party, and each box contains 6
donuts. How many boxes must you order if each person eats 3 donuts? You need to figure this
out quickly. Well, the best thing to do is to apply dimensional analysis like this:
