Chapter 1, Problem 1GST

To determine

To calculate: The percentage or fraction of geological timescale that is represented by the recorded history of human kind.

Answer to Problem 1GST

The percentage of geological timescale represented by the recorded history of human kind is $0.0001\raisebox{1ex}{$0$}\!\left/ \!\raisebox{-1ex}{$0$}\right.$.

Explanation of Solution

Given info:

The length of recorded history for humankind is about $5000\text{years}$ and the age of the Earth is $4.5\text{billion}\text{years}$ that can be approximated as $5\text{billion}\text{years}$.

We know that $1\text{billion}{\text{=10}}^9\text{years}$, therefore $5\text{billion}\text{years}\text{=5}\times {\text{10}}^9\text{years}$.

The expression for calculating the fraction of geological timescale represented by the recorded human history,

$\text{Fraction}\text{of}\text{timescale}\text{denoted}\text{by}\text{recorded}\text{human}\text{history}\text{=}\frac{\text{Length}\text{of}\text{recorded}\text{human}\text{history}}{\text{Age}\text{of}\text{the}\text{Earth}}$

Substitute $5000\text{years}$ for the length of recorded human history and $\text{5}\times {\text{10}}^9\text{years}$ for the age of Earth in the above expression.

$\begin{array}{c}\text{Fraction}\text{of}\text{timescale}\text{denoted}\text{by}\text{recorded}\text{human}\text{history}\text{=}\frac{\text{5000}\text{years}}{5\times {10}^9\text{years}}\\ =0.000001\end{array}$

The expression for calculating the percentage of the fraction denoted by recorded human history, $\text{Percentage of the fraction}\text{of}\text{timescale}\text{denoted}\text{by}\text{recorded}\text{human}\text{history}\text{=Fraction}\text{of}\text{human}\text{history}\times 100$

Substitute $0.000001$ for the fraction of human history in the above expression.

$\begin{array}{c}\text{Percentage of the fraction}\text{of}\text{timescale}\text{denoted}\text{by}\text{recorded}\text{human}\text{history}=0.000001\times 100\\ =0.0001\raisebox{1ex}{$0$}\!\left/ \!\raisebox{-1ex}{$0$}\right.\end{array}$