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# How do you convert 12.6g/cm^3 to kg/m^3?

I did 12.6g/cm^3 * 1,000,000cm^3/m^3 * kg/1000g = 12,600kg/m^3 which I know is wrong

### 5 Answers

- 9 years agoFavorite Answer
12.6 g/cm^3 * (1 kg / 1000 g) * (100 cm / 1 m) ^3

(grams cancel out, but we'll leave the (100 cm / 1 m)^3 term in case you don't understand)

= 0.0126 kg/cm^3 * (1000000 cm^3 / 1 m^3)

this is because everything in the (100 cm / 1 m) term is cubed

= 12600 kg/m^3

though, due to significant figures, it's more properly

1.26*10^4 kg/m^3

Your answer was right, except perhaps that it wasn't in scientific notation because you should account for significant figures. What made you think you were wrong?

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- Anonymous9 years ago
Actually you are correct.

I prefer to use scientific notation to avoid possible errors

(12.6 g/cm^3)(1.00 x 10^2 cm/m)^3 (1.0 kg/1.00 x 10^3 g) = 12.6 x 10^3 kg/m^3

= 12,600 kg/m^3

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- 9 years ago
no, it's correct.

1 g = 10^-3 kg

1 cm^3 = 10^-6 m^3

then, 12.6 g/cm^3 = 12.6 * 10^-3 kg / (10^-6 m^3) = 12.6 * 10^-3 * 10^6 kg/m^3 = 12.6 * 10^3 kg/m^3

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- 9 years ago
You are correct:

12.6g----|--(100)^3 cm^3--|--1 kg

-----------------------------------------------

1 cm^3--|------1^3 m^3-----|-1000g

= 12, 600 kg/m^3 or 1.26 x 10^4

professional calculation by google confirms it: http://www.google.com/search?aq=f&sourceid=chrome&...

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