Does 1 Joule of Energy Have a Distinct Mass?

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Homework Statement



The equation E=mc^2 and its counterpart m=E/c^2 state that energy and matter are the same thing. (kinda stupid question) Does that mean that 1 joule of energy has a mass? Am I wrong in thinking this? (more to the point, does 1 unit of energy have a distinct mass)

Homework Equations



m=E/c^2
1 joule=1kg(m/s)^2

The Attempt at a Solution



m=1joule/c^2
m=1kg(m/s)^2/299792458 m/s^2
m=1kg(m/s)^2/89875517873681764(m/s)^2
m=1kg/89875517873681764
m=1.112650056053618432174089964848e-17kg

so 1 joule of energy has 1.112650056053618432174089964848e-17kg of mass?
 
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thank you for that link. I will most likely completely read the whole thing through. hopefully it will state weather matter and energy are the same thing or just that they can be converted into each other.