The jump-like behavior of coordinates of planets and the Moon as well as of their derivatives retrieved from modern ephemerides is demonstrated. Discontinuities of the coordinates and derivatives take place at the junctions of the adjacent interpolation intervals each of which in the ephemerides has its own set of the coefficients of the Chebyshev polynomials. This is demonstrated on an example of the ephemerides DE431 and EPM2011. The precision of predicted motion of asteroids is estimated with allowance for perturbations from the ephemerides DE431 and EPM2011. It is demonstrated that the step of numerical integration of the equations of motion must be adjusted to the junctions of the ephemeris intervals; in this case, the precision of integration increases by several orders of magnitude. In addition, to eliminate discontinuities of the coordinates and of their first derivatives arising in calculations with quadruple precision, an algorithm of smoothing ephemerides at the junctions of interpolation intervals is developed that allows the discontinuities of the coordinates and their derivatives up to any preset order to be eliminated. The algorithm is used to smooth the ephemerides DE431 and EPM2011 up to the fourth-order derivatives. It is demonstrated that in calculations with the quadruple precision, the application of the smoothed ephemerides allows the accuracy of numerical integration to be increased approximately by 10 orders of magnitude.