The purpose of this paper is to compare a new method called Embedded Monte Carlo (EMC) to the well-known Total Monte Carlo (TMC) method for nuclear data uncertainty propagation. Indeed, the TMC methodology is based on the use of a large number of random samples of nuclear data libraries and performing separate Monte Carlo calculations for each random sample. Then, the computation of nuclear data uncertainty is based on the difference between the total uncertainty and the statistical uncertainty of each Monte Carlo simulation. This method can either be applied to MC and deterministic codes where there are no statistical uncertainties. The goal of EMC is to compute statistical uncertainty for each random sample by utilizing historical statistics instead of the batch statistics employed in TMC. Consequently, one large Monte Carlo simulation can be conducted where each batch represents a new random sample, thereby embedding the propagation of uncertainties within a single calculation and reducing computational expenses. This approach allows for the calculation of nuclear data uncertainty using history statistics in fixed source and eigenvalue calculations. This paper demonstrates the capability of this new method using OpenMC. The analysis will be performed on a Godiva sphere benchmark by propagating the uncertainty on two input parameters: the average neutron multiplicity ν and ²³⁵U density.