Chapter 1, Problem 1PQ

The average life expectancy in Japan is 81 years. What is this time in SI units?

To determine

The average life expectancy in place J in SI units.

Answer to Problem 1PQ

The average life expectancy in place J in SI unit is $2.6\times {10}^9\text{s}$.

Explanation of Solution

The average life expectancy in place J is given in years. The SI unit of time is second.

Write an expression for converting the average life expectancy in place J in years to seconds.

  $t_s=t_y\left(\frac{365\text{day}}{1\text{y}}\right)\left(\frac{24\text{h}}{1\text{day}}\right)\left(\frac{60\text{min}}{1\text{h}}\right)\left(\frac{60\text{s}}{1\text{min}}\right)$        (I)

Here, $t_s$ is the average life expectancy in place J in seconds and $t_y$ is the average life expectancy in place J in years.

Conclusion:

Substitute $81\text{y}$ for $t_y$ in equation (I) to find $t_s$.

    $\begin{array}{c}{t}_s=\left(81\text{y}\right)\left(\frac{365\text{day}}{1\text{y}}\right)\left(\frac{24\text{h}}{1\text{day}}\right)\left(\frac{60\text{min}}{1\text{h}}\right)\left(\frac{60\text{s}}{1\text{min}}\right)\\ =\left(81\text{y}\right)\left(3.15\times {10}^7\text{s/y}\right)\\ =2.6\times {10}^9\text{s}\end{array}$

Thus, the average life expectancy in place J in SI unit is $2.6\times {10}^9\text{s}$.