3
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$$\ce{H2SO4 + CaCO3 -> H2CO3 + CaSO4}$$

I thought it would be a double replacement and also a decomposition reaction because $\ce{H2CO3}$ immediately breaks down to $\ce{H2O}$ and $\ce{CO2}$.

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    $\begingroup$ The decomposition part is not portrayed in your equation so you can't say that the equation contains decomposition. $\endgroup$ – DHMO Jan 18 '17 at 23:44
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While double replacement is correct, you could also classify it as a neutralization reaction (what I think would be the most common answer if one had to pick a single description). I agree with the comment explaining that you can't consider it a decomposition reaction as written. You would need to explicitly show that as part of the reaction for that to be an acceptable description.

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