Converting from cm² to m² is a very simple task that can be learned in no time. The fundamental thing that is needed to know to transform one unit of measurement into another is the respective equivalence between said units.
In this particular case, the equivalence that needs to be known is the one between centimeters and meters.
The quadratic power that appears in the units is not something to worry about, since what matters is the unit of measurement with which you are working.
The technique that will be used in this article to transform from cm² to m² can be imitated to transform other units of measurement, always keeping in mind the correspondence between the units to be converted.
To go from cm² to m², what is done is to transform «cm» to «m», and the result is squared to achieve the objective.
How to convert from cm² to m²?
Since the equivalence between the units of measurement is fundamental, this equivalence is described below:
- 1 meter represents the same length as 100 centimeters.
- 1 square meter (1m²) is then equal to 100cm * 100cm = 10,000 cm².
Knowing the equivalence, what continues is the conversion method.
Conversion
It starts from the assumption that the quantity to be converted is P cm², where P is any number.
To go from cm² to m², the entire quantity must be multiplied by 1 square meter (1 m²), and divided by 10 000 square centimeters (10 000 cm²).
Therefore, P cm² is the same as
P cm² * (1 m² / 10 000 cm²) = P * 0.0001 m².
What you need to do for the measurement conversion is to divide by the unit of measurement that you want to eliminate and multiply by the equivalent unit of measurement to which you want to arrive.
Examples
First example
Juan bought an apartment whose dimensions are 550,000 cm². What are the dimensions of the apartment in meters?
To answer it is necessary to convert the units of measure. Using the previous formula it turns out that:
550,000 cm² = 500,000 cm² * (1m / 10,000 cm²) = 55 m².
Therefore, the dimensions of the apartment are 55 m².
Second example
Maria wants to buy a rectangular gift card, whose measurements are 35 cm long and 20 cm wide. What is the area of the card in square meters?
In this exercise, the area of the gift card is asked, which because it is a rectangle is equal to the length of the length multiplied by the length of the width. That is, the area is A = 35cm * 20cm = 700 cm².
To calculate the area in square meters, we proceed to the conversion of the units using the previous formula:
700 cm² = 700 cm² * (1 m² / 10,000 cm²) = 7/100 m² = 0.07 m².
In conclusion, the area of the card is 0.07 m².
Third example
Martín and Carlos planted vegetables on their land. Martín's land is 30 meters long and 50 wide, while Carlos's is 3000 cm long and 4500 cm wide. Which field will have the most vegetables by harvest time?
The area of Martín's land is 30m * 50m = 1,500m². On the other hand, it is more convenient to convert Carlos's terrain measurements rather than calculate his area.
Using the conversion formula you have to:
3000 cm = 3000 cm * (1m / 100cm) = 30 m
4500 cm = 4500 cm * (1m / 100cm) = 45 m
Therefore, the area of Carlos's land is 30 * 45 m² = 1350 m².
In conclusion, by harvest time Martín's field will have more vegetables, since it is larger.
References
- Díaz, MG (2008). Unit Conversions in Climatology, Meteorology and Atmospheric Pollution. Humanities Editorial Fund.
- Díaz, RG, & Garcia, R. (1998). Engineering Formulas Manual. Editorial Limusa.
- Giancoli, D. (2006). Physics Volume I. Pearson Education.
- Jaramillo, ME, Herrera, Á. M., & Montoya, CE (sf). Unit conversion table. Metropolitan Technological Institute.
- Tipler, PA, & Mosca, G. (2005). Physics for Science and Technology, Volume 1. Reverte.