Question

A student converted centimeters to kilometers in the following way:
http://media.apexlearning.com/Images/201305/31/61d61d24-3736-4b93-aedd-f151ba228ee2.gif
Is this correct? If not, what is the correct way to convert centimeters to kilometers?
A.http://media.apexlearning.com/Images/201305/31/3a67ab91-bab5-48b9-bba9-cb085ce17c77.gif
B.http://media.apexlearning.com/Images/201305/31/3e581560-a632-4e72-a053-cf38c6cac049.gif
C. The student was correct: http://media.apexlearning.com/Images/201305/31/94c44284-cfc4-40de-adf7-e5b802035c92.gif
D.http://media.apexlearning.com/Images/201305/31/6

Answer 1

D. http://media.apexlearning.com/Images/201305/31/6b557d5f-80a5-4a6e-abda-19069b76bcef.gif

Answer 2

Would you mind showing how YOU would make this conversion?
How many cm are there in 1 m? How many m are there in 1 km?

Answer 3

1m = 100cm

1km = 1000m

Answer 4

@mathmale

Answer 5

Correct.

Answer 6

so the answer is D

Answer 7

Your conversion factors are fine. Please, use them come up with a new "cm to km" conversion factor. Please show your work.

Answer 8

Hint* if you just forget about the numbers for now and focus only on the units

we have

\[\large cm(\frac{cm}{m})(\frac{m}{km})\]
If we multiply everything through we get:
\[\large \frac{cm^2\times m}{m\times km}\]
Cancelling what we can...we have
\[\large \frac{cm^2}{km}\]

Not quite what we want...how can we change the original expression to get us to the units we want?

Answer 9

so would we flip it

Answer 10

Flip what specifically?

Answer 11

put cm on top and m on bottoms and put m on top and km on bottoms

Answer 12

What you have written above is exactly what is happening in the original question

*I think you just worded it wrong :) Looking back at the original...Notice we DO have cm on top and m on bottom etc...so what do we need?

Answer 13

okay so we need to put m on top and cm on bottom and put km on top and cm on bottom

Answer 14

THERE we go! *You wrote "cm on bottom" in the second part but I'll just take that as a typo where you meant 'm' :)

If we do that...we get:

\[\large cm(\frac{m}{cm})(\frac{km}{m})\]

Multiplying through:

\[\large \frac{cm\times m \times km}{cm \times m}\]

or just \(\large km\)

GREAT!

Now just add in the numbers!

\[\large 1cm(\frac{1m}{100cm})(\frac{1km}{1000m}) = ?\]

Answer 15

so it would be D. ? = 0.00001km

Answer 16

Correct :)