Example 1. The following numbers are all approximate numbers obtained by rounding. Find their absolute error bounds and relative error bounds:
$$
\begin{array}{l}
\text { (1) } \mathrm{a}_{1} \approx 12.5, \quad(2) \mathrm{a}_{2} \approx 1.25 \times 10^{4}, \\
\text { (3) } \mathrm{a}_{3} \approx 0.0125
\end{array}
$$
$\begin{array}{c}\text { Solution (1) } \boldsymbol{\delta}_{\mathrm{a}_{1}}=0.05, \\ \boldsymbol{\delta}^{\prime}{ }_{\mathrm{a}_{1}}=\frac{0.05}{12.5}=0.4 \% ; \\ \text { (2) } \boldsymbol{\delta}_{\mathrm{a}_{2}}=50, \\ \boldsymbol{\delta}^{\prime}{ }_{\mathrm{a}_{2}}=\frac{50}{12500}=0.4 \% ; \\ \text { (3) } \boldsymbol{\delta}_{\mathrm{a}_{3}}=0.00005, \\ \boldsymbol{\delta}^{\prime} \mathrm{a}_{3}=\frac{0.00005}{0.0125}=0.4 \% .\end{array}$