Problem about units conversion: cm^2 --> m^2

[inuka00123]

Homework Statement

I need to find how much meters equal to area of 100cm²

Relevant Equations

100cm = 1m
10cm = 1/10m = 0.1m
10cm² ≠ (1/10m)² = (0.1m)²

in the problem 100 cm is obviously equal to 1m, and 10cm is equal to 1/10m and it is equal to 0.1m, but when you take the square of the 10cm it is obviously does not equal (1/10m)² nor (0.1m)², therefore (10cm x 10cm ≠ 1/10m x 1/10m = 0.1m x 0.1m), then to what 10cm x 10cm is equal to in meters? 1/100m or 0.01 meters does not equal to 100cm, this problem seems really easy, but I've tried come up with solution but I wasn't able to. if I take off the units it is obvious that one doesn't not equal to other, any help would be really appreciated.

 

[haruspex]

when you take the square of the 10cm it is obviously does not equal (1/10m)²

If $x=y$ then $x^2=y^2$.
If $10cm=(1/10)m$ then what is $(10cm)^2$?

 

[jack action]

1/100m or 0.01 meters does not equal to 100cm

No, it is 0.01 m² = 100 cm². The exponent on the units is important:

• (0.1 m) X (0.1 m) = (0.1 X 0.1) (m X m) = 0.01 m.m = 0.01 m²;
• (10 cm) X (10 cm) = (10 X 10) (cm X cm) = 100 cm.cm = 100 cm².

You can even have uncommon units like (0.1 m) X (10 cm) = (0.1 X 10) (m X cm) = 1 m.cm which is also equal to 0.01 m² or 100 cm².