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We present a model of quantum metrology inspired by the computational model known as deterministic quantum computation with one quantum bit (DQC1). Using only one pure qubit together with l fully mixed qubits we obtain measurement precision (defined as root-mean-square error for the parameter being estimated) at the standard quantum limit, which is typically obtained using the same number of uncorrelated qubits in fully pure states. In principle, the standard quantum limit can be exceeded using an additional qubit which adds only a small amount of purity. We show that the discord in the final state vanishes only in the limit of attaining infinite precision for the parameter being estimated.