When converting a measurement in cm to a measurement in km. For example 20.7 cm when I switch that to decimeters its 2.07 dm then .207 m. Then deka meter .0207 then hecto .00207 then kilometer .000207 km 2.07e-4 km However my book says its 2.07e-9 km. How is that happening? What am I missing?

Question

anonymous · Answer

You are correct according to your post.
You sure the problem is not asking you to convert $$20.7cm^2 \to km^2$$

anonymous · Answer

That is what its asking. lol I figured that the squared didn't matter. Seeing as both are squared I thought I could deal with the numbers independently.

anonymous · Answer

So im guessing that the squared has something to do with why im confused but what about it being squared changes my answer?

anonymous · Answer

cm2=(cm)(cm)
 and 
km2=(km)(km)

Start with given variable and units
Solve for the unknown units.
Try to make the starting units cancel out by multiplying the cm in denominator twice.
You want km^2 so multiply the km twice by putting it as a numerator over the cm.

So it equals to this

 
$$\frac{ 20.7cm^2 }{ 1 }\times \frac{ ?km }{ 1cm }\times \frac{ ?km }{ 1cm }$$

Fraction and numerator should equal after starting out the given variable.
Since 0.00001km=1cm then it
$$\frac{ 20.7cm^2 }{ 1 }\times \frac{ 0.0001km }{ cm }\times \frac{0.0001km }{ cm }$$

Multiply it and the cm units would cancel out leaving you with just the km^2 and it would be 0.000000000207km or 2.07 x 10^-9km or 2.07e^-9

anonymous · Answer

20.7 * 0.0001 * 0.0001 = 0.000000207 = 2.07e-7 
How am I still missing this?

anonymous · Answer

I made a typo, supposed to be 20.7km*0.00001km*0.00001km=
I made no typo explaining,just in the conversion example.