The \(\frac{^{143}Nd}{^{144}Nd}\ \text{and}\ \frac{^{147}Sm}{^{144}Nd}\) ratios of a rock are 0.516 and 0.389, respectively. The rock evolved as a closed system. As per the exact parent-daughter relationship \(\frac{^{143}Nd}{^{144}Nd}\) equation, the ratio of the rock 4.6 × 109 years ago was ______. (Round off to three decimal places)
(Use decay constant for 147Sm = 6.54 × 10-12 y-1)