Science Question.

Question

Why can we multiply by 100 cm/1 m and not change the true value of the number? 

Answer 1

I would recommend Googling the term "dimensional analysis". This is the field you are currently questioning and there are a lot of good articles on it.

To put it simply here though, you are just converting units from one to another. Let's say I have a pole that is 3 m long. Since I know that there are 100 cm in 1 m, then I know my pole is also 300 cm. I can say my pole is 3 m long or 300 cm long and both would be correct. I can convert the length of 3 m to any unit of length I choose, just as long as I know the conversion number. Here is our example written out:

3 m * 100 cm / 1 m = 300 cm

Notice how the meter unit for the 3 m cancels out with the 1 m that is in the denominator of that number, leaving us with the unit of cm. That's how a conversion works. You can do this with any unit of measure depending on what you are looking for. Let's say you wanted to know the length of the pole in feet. This is what you do.

3 m * 3.28 ft / 1 m = 9.84 ft

Now, let's do one more complicated. Let's say I'm driving a car at 60 miles per hour . What is that in meters per second? Let's write it out.

[60 miles / 1 hour] * [5280 feet / 1 mile] * [1 m / 3.28 feet] * [1 hour / 60 minutes] * [1 minute / 60 seconds] = 26.83 m/s

Notice how I use the units to cancel out the previous units and get to what I want. The units change every time I multiply a new term, and they change like this:

1. Term 1: miles per hour
2. Term 2: feet per hour
3. Term 3: meters per hour
4. Term 4: meters per minute
5. Term 5: meters per second

You can say these conversion terms all equal one, because your just dividing the term by itself. If 100 cm = 1m, then 100 cm / 1 m = 1 m / 1 m = 1. These values do not change the actual value, just put it into units you want.