Sometimes we get a result whose mantissa is greater than 1.0:

           0.56740 x 105
     +     0.48293 x 105
     -------------------
           1.05033 x 105

When this happens, it might appear that we have overflow, but the sum's mantissa can be shifted to the right and 1 added to the exponent:

          0.10503 x 106

When we do this, we will lose some precision because the rightmost (least significant) digit of the mantissa will be lost. As always with floating point numbers, there is a trade-off between representation of magnitude and precision, since there is only a fixed number of bits to work with.