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We introduce a new cryptosystem based on decimal numbers. A secret key is shared between A and B to construct their decimal public keys. The secret key is distributed through the classic Deffie-Hellman protocol but after a modification that is introduced in order to enable this protocol to work on decimal numbers. The modification is applied by extends the theory of the modulus to be applicable on real numbers. We prove that there is no loss of any bit of information during the encryption and the decryption by introducing and proving a new concept that we call the rounding off theorem.