converting meters to centimeters

[puttonen04]

How do I do this problem: A Tackle box is .2 meters wide and .45 meters lon. What is the area in cm?

The first thing we did was to multiply .45 by .2 and we got 0.09. Not sure what to do next.

 

[JeffM]

How do I do this problem: A Tackle box is .2 meters wide and .45 meters lon. What is the area in cm?

The first thing we did was to multiply .45 by .2 and we got 0.09. Not sure what to do next.

There is nothing wrong with the way you started, but it is a lot easier to convert to centimeters first.

\(\displaystyle 0.2m * \dfrac{100cm}{m} = 20cm\ and\ 0.45m * \dfrac{100cm}{m} = 45cm \implies 20cm * 45cm = 900cm^2.\)

An area must be in square meters or square centimeters or square something.

Now you can do the problem your way, but then you cannot use the easy to remember conversion factor of 100 centimeter per meter.

\(\displaystyle 0.2m * .45m = .09m^2 \implies .09m^2 * \dfrac{10,000cm^2}{m^2} = 900cm^2.\)

Where did that conversion factor of 10,000 square centimeters per square meter come from:

\(\displaystyle \dfrac{100cm}{m} * \dfrac{100cm}{m} = \dfrac{10,000cm^2}{m^2}.\)

Follow?

 

[HallsofIvy]

Another way to do this (and avoid decimal fractions) is to convert the linear measurements first.
There are 100 cm in a m so .2 meters is .2(100)= 20 cm and .45 meters is .45(100)= 45 cm.
The area is (20 cm)(45 cm)= 900 square cm.