How do I convert cubic picometer to cubic centimeter?

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Homework Help Overview

The discussion revolves around converting cubic picometers to cubic centimeters, specifically focusing on the volume calculation of a unit cell with a given edge length of 288 picometers.

Discussion Character

  • Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants explore the calculation of volume by cubing the edge length in picometers and converting it to centimeters. There is confusion regarding the intermediate steps and the final result of 2.39 x 10^-23 cm³.

Discussion Status

Some participants are attempting to clarify the cubing process and the conversion from picometers to centimeters. Various approaches to the calculation are being discussed, but there is no explicit consensus on the reasoning or the final outcome.

Contextual Notes

Participants are working under the constraints of homework rules, which may limit the amount of direct assistance they can provide to one another.

Rajdeep Biswas
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moved into the homework section, therefore no template shown
Part of the question says: An unit cell has a cell edge of 288 pm.
I got to the part where volume (288 pm)^3 = (288 x 10^-10 cm)^3
I have no idea how that equals 2.39 x 10^-23 cm^3

Only the Bold part ^
 
Last edited by a moderator:
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##288^3=2.39 \cdot 10^{7}##
 
Rajdeep Biswas said:
... (288 x 10^-10 cm)^3
I have no idea how that equals 2.39 x 10^-23 cm^3

I'm a little confused. Plug 288x10^-10 into your calculator and hit the cubed button. If you would like to do it in your head try

(288e-10)^3 = (2.88e-8)^3
= 2.88^3 x (10^-8)^3
= 2.88^3 x 10^-24
= (3-0.12)^3 x 10^-24
= (3^3 - 3*3^2*0.12 + small) x 10^-24
~= 27*(1-0.12) x 10^-24
~= (27-2.7-0.54) x 10^-24
= 2.376 x 10^-23
 
(288 * 10-10)3
= 2883 * (10-10)3
= 2.39 * 107 * 10-10 * 10-10 * 10-10
= 2.39 * 10-23
 

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