How should I find the area of a square in meters when the sides are in millimeters?Should I first convert the sides to meters or should i first calculate with the sides still in millimeters and...

How should I find the area of a square in meters when the sides are in millimeters?

Should I first convert the sides to meters or should i first calculate with the sides still in millimeters and then convert the answer to millimeters?

Expert Answers
sciencesolve eNotes educator| Certified Educator

You may proceed both ways, either you convert the length of side of square in meters and then you substitute the converted value in formula of area, or you calculate the area first, then you convert the result from milimeters to meters.

You need to solve a problem using both methods to convince yourself that you will get the same result.

You need to consider the value of length of square side `x = 5 mm` .

Converting from milimeters to meters yields: `x = 0.005 m` .

You need to evaluate the area of the square such that:

`A = x*x m^2`

Substituting `0.005`  for x yields: `A = 0.000025 m^2`

You should solve this problem using the second method, hence you need to calculate the area first, then you need to convert the result from milimeters to meters such that:

`A = 5mm*5mm = 25 mm^2`

You need to remember that `1mm = 10^(-3) m` , hence `1mm^2 = (10^(-3))^2 m = 10^(-6)m`

You need to convert `25 mm^2`  into `m^2` , hence you need to multiply by `10^(-6` ) such that:

`A = 25*10^(-6) = 25/(10^6) =gt A = 0.000025 m^2`

Hence, both results prove that both methods work to find the area in meters, if length of the sides are given in milimeters.

najm1947 | Student

It hardly matters becuase the conversion is very simple for area:

1 m = 1000 mm = 1*10^3 mm

1 m2 = 1*10^3 * 1*10^3 = 1*10^6 mm2

In case you start with mm, you get the area in mm2 and to convert area in mm2 to m2 you divide the area in mm2 by 10^6

In case you prefer to start with convering the length of a side from mm to meters, the answer for area will be in m2 withour any subsequent conversion.

 

atyourservice | Student

You can do it both ways, it doesnt matter if you convert after solving or before solving the answer will be the same.