Calculating TNT Needed to Match Energy of 1 Gram U-235

[Cudi1]

Homework Statement

Nuclear energy changes are significantly greater than chemical changes. The detonation of 1.00 g of the explosive trinitrotoluene (TNT) releases 2.760 kJ. How many grams of TNT would be needed to match the energy released by one gram of U-235?
( 1 gram of U-235 contains 2.56*10^21 nuclei)

Homework Equations

The Attempt at a Solution

Basically, it is a continuation of the previous question in which i found that the amount of energy released in fission of U-235 nucleus is 2.82*10^-11J.
what i did was multiply (2.82*10^-11)(2.56*10^21)= 7.22*10^7kJ, i then divided that amount
7.22*10^7kJ/2.760kJ= 2.6*10^7 ( although the units are not in grams , what am i doing wrong)

 

[phyzguy]

I think you did it right. I checked Wikipedia ( http://en.wikipedia.org/wiki/Energy_density), and I also find the ratio of the energy density of these two materials to be ~2E7. Why do you think it is wrong? Your final answer is a ratio, so it is unitless.