called Dimensional Analysis)
problems use multiplication of the labels to convert from one label to another.
2 years into seconds.
writing down the given information
make sure there is a numerator (top)& denominator
Since this is called the Factor-Label Method we must multiply, but only with a
With years in the numerator we must multiply by
something with years in the denominator.
to come up with a numerator, we use a thing called a conversion factor.
Factors are constructed by
placing 2 equal values on top of each other.
all know that 7 ÷ 7 = 1 and
4 ÷ 4 = 1
did you know that 1 gallon ÷ 4 quarts = 1 ???
5 pennies ÷ 1 nickel = 1 ???
may have guessed what our 1st conversion factor will be:
ask, “Why are the days on top and the years on the bottom?
The whole reason factor-label problems work is
because we are going to cancel the labels.
at the problem above, we can see that we have years on the top of the 1st
factor and years on the bottom of the second factor.
stop now we would have:
we know that
= 1 we also
same label is on top of one factor and on the bottom of another then they will
combine to make one.
and dividing by one does not change a number.
multiplying and dividing by one doesn’t change anything then it doesn’t make
much sense to do it.
we cancel them out and continue on with our problem.
were asked to find how many seconds are in 2 years so we must make our label
smaller than days.
most people don’t know how many seconds are in 1 day, we use what we know.
know that 1 day = 24 hours
a conversion factor out of this equality by putting one on top of the other.
but which way?
problem currently has days in the numerator, so we need days to be in the
This allows us to cancel the label days.
still don’t have seconds, so we keep multiplying & canceling until the
only label left in our problem is seconds.
very few of us know how many seconds are in and hour we must convert hours into
This allows us to cancel the label hours.
this point our label is minutes, so we keep multiplying & canceling until
the only label left in our problem is seconds.
we have seconds as our only label!
is when we grab a calculator and start the math that will give us a number to
put in front of the seconds label.
must multiply across the top of our problem.
multiply across the bottom of our problem.
this we take the top and divide it by the bottom
and put our seconds label on the answer.
is our completed problem.
There are 63,115,200 seconds in 2 years.
Learn more about Metric Prefixes
places to look for more help
Learn how to convert one unit of measure into
another unit of measure
Factor-Label Examples & Practice Problems
On this page you will find many helpful links to help you understand the Metric System (SI) and to convert within it and between US measurements and SI.
Simple Online Converter with conversion factors visible
Online Converters dozens of online converters
many Online converters
Very Nice! Interactive Units Converters - Puzzles - Periodic Table - Constants
Dozens of online converters. Very Nice!
Several online converters.
Common Equivalent Weights and Measures
Weather Conversion Calculators just what you would expect
A Dictionary of Units provides a summary of most of the units of measurement in use around the world today
A Dictionary of Measures, Units and Conversions
Significant Figures in Measurements and Calculations good info
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