Metric Conversions

Factor-Label Problems

(also called Dimensional Analysis)

Factor-Label problems use multiplication of the labels to convert from one label to another.

Example:

Convert 2 years into seconds.

Start by writing down the given information

make sure there is a numerator (top)& denominator (bottom).

Next: Since this is called the Factor-Label Method we must multiply, but only with a purpose.

With years in the numerator we must multiply by something with years in the denominator.

In order to come up with a numerator, we use a thing called a conversion factor.

Conversion Factors are constructed by

placing 2 equal values on top of each other.

We all know that 7 ÷ 7 = 1  and  4 ÷ 4 = 1

But, did you know that 1 gallon ÷ 4 quarts = 1 ???

Or 5 pennies ÷ 1 nickel = 1 ???

So you may have guessed what our 1st conversion factor will be:

You may 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.

Looking at the problem above, we can see that we have years on the top of the 1^st factor and years on the bottom of the second factor.

If we stop now we would have:

Since we know that = 1     we also know that = 1

If the same label is on top of one factor and on the bottom of another then they will combine to make one.

Multiplying and dividing by one does not change a number.

If multiplying and dividing by one doesn’t change anything then it doesn’t make much sense to do it.

So we cancel them out and continue on with our problem.

We were asked to find how many seconds are in 2 years so we must make our label smaller than days.

Since most people don’t know how many seconds are in 1 day, we use what we know.

We know that 1 day = 24 hours 

We make a conversion factor out of this equality by putting one on top of the other.

                                          but which way?                 

Our problem currently has days in the numerator, so we need days to be in the denominator.

This allows us to cancel the label days.

We still don’t have seconds, so we keep multiplying & canceling until the only label left in our problem is seconds.

Since very few of us know how many seconds are in and hour we must convert hours into minutes.

This allows us to cancel the label hours.

At this point our label is minutes, so we keep multiplying & canceling until the only label left in our problem is seconds.

Now we have seconds as our only label!

This is when we grab a calculator and start the math that will give us a number to put in front of the seconds label.

We must multiply across the top of our problem.

Then multiply across the bottom of our problem.

After this we take the top and divide it by the bottom
and put our seconds label on the answer.

This is our completed problem.
There are 63,115,200 seconds in 2 years.