1-14 할리데이 10판 솔루션 일반물리학

$$ \%=100\times \frac{(\text{TrueValue}-\text{ApproxValue})}{\text{TrueValue}} $$
(a) $1\ut{\mu Centry} = ?$ $$ \begin{aligned} & 1\ut{\mu Centry} \\ &= 1\times 10^{-6}\ut{Centry} \cdot \frac{100\ut{years}}{1\ut{Centry}} \cdot \frac{365.2422\ut{days}}{1\ut{years}}\cdot \frac{24\ut{h}}{1\ut{days}}\cdot \frac{60\ut{min}}{1\ut{h}} \\ &= 1\times 10^{-6}\cdot100\cdot 365.2422\cdot 24\cdot 60\ut{min} \\ &= \frac{16435899}{312500}\ut{min} \\ &= 52.5948768\ut{min} \\ &\approx 50\ut{min} \end{aligned} $$
(b) $$ \begin{cases} \text{TrueValue} &= \frac{16435899}{312500}\ut{min} \\\text{ApproxValue} &= 50\ut{min} \end{cases} $$ $$ \begin{aligned} \%&=100[\%]\times \frac{(\text{TrueValue}-\text{ApproxValue})}{\text{TrueValue}} \\ &= 100[\%]\times \frac{\left(\frac{16435899}{312500}\ut{min}-50\ut{min}\right)}{\frac{16435899}{312500}\ut{min}} \\ &= \frac{81089900}{16435899}[\%] \\ &\approx 4.9337063947642900458[\%] \\ &\approx 5[\%] \end{aligned} $$