Tubular reactor for a thermal cracking are designed on the assumption of plug flow. On the suspicion that non$-$ideal flow may be an important factor now being ignored, dispersion number was estimated to be $0\mathrm{.}10.$ The cracking reaction is approximately first order. If calculations show that $99\%$ decomposition can be obtained in a plug flow reactor $3$ m long, how much longer must the real reactor be of non ideal flow is considered?