Question

Be sure to show all calculations clearly and state your final answers in complete sentences. Geological time scales are often written in ways that can mask their significance. For each of the following pairs of times, state which one is larger and by how much: a. 25,000 years, 0.1 million years b. 4 million years, 0.05 billion years c. 0.1 billion years, 1 million years

Short answer

a. 0.1 million years is larger by 0.075 million years; b. 0.05 billion years is larger by 0.046 billion years; c. 0.1 billion years is larger by 99 million years.

Step-by-step solution

Convert Years to Million Years (Part a)

First, let's convert both numbers into the same unit, typically million years, for easy comparison.1. 25,000 years = \( \frac{25,000}{1,000,000} \) million years = 0.025 million years.2. 0.1 million years remains 0.1 million years as it is already in million years.

Compare Values (Part a)

Now that both quantities are in million years, compare them: 0.1 million years is larger than 0.025 million years by \( 0.1 - 0.025 = 0.075 \) million years.

Convert to Comparable Units (Part b)

Convert the given times into the same unit: either million years or billion years.1. 4 million years = \( \frac{4}{1,000} \) billion years = 0.004 billion years.2. 0.05 billion years remains 0.05 billion years.

Compare Values (Part b)

With both values in billion years:0.05 billion years is larger than 0.004 billion years by \( 0.05 - 0.004 = 0.046 \) billion years.

Convert to Million or Billion Years (Part c)

Convert the given values: 1. 0.1 billion years = 0.1 × 1000 million years = 100 million years. 2. 1 million year remains as 1 million year.

Compare Values (Part c)

Now that both values are in million years:100 million years is larger than 1 million year by \( 100 - 1 = 99 \) million years.

Key concepts

Unit Conversion

Unit conversion is a crucial mathematical process that allows us to transform quantities from one unit of measurement to another. This is important in various fields, including geology, where time is often expressed in different units like years, million years, and billion years.
To effectively compare geological time, we need to convert different time units to a common base. For instance, to compare 25,000 years with 0.1 million years, we convert 25,000 years to million years by dividing by 1,000,000, resulting in 0.025 million years. Now that both times are in the same unit, we can easily compare them.
Understanding unit conversion helps in grasping the differences in magnitudes and appreciating the vastness of geological time scales. This is not just a mathematical exercise but also enhances our perception of Earth's history.

Million Years

In geosciences, million years is a widely used unit of time to mark significant geological events. It provides a scale for understanding processes that shape our planet over vast periods. For calculations involving million years, a million years is equal to 1,000,000 years.
When comparing time periods, converting smaller units (like years) into million years facilitates easier comparison and better understanding. In the example of comparing 25,000 years and 0.1 million years, turning both into million years lets us see that 0.1 million years equates to a much longer period than 25,000 years.
The simplicity of using million years lies in its ability to handle large numbers more practically, making complex and lengthy comparisons more manageable for us.

Billion Years

The unit of billion years is frequently employed in discussions about Earth’s history, the age of the solar system, or the universe. It represents a billion (1,000,000,000) years. This unit is essential for capturing the full scope of long-term geological processes.
Comparing million years to billion years involves converting the smaller unit to the larger; for instance, 4 million years can be converted to 0.004 billion years. This allows direct and straightforward comparison with other quantities already in billion years. Thus, in the given exercise, comparing 4 million years with 0.05 billion years is simplified by expressing both in billion years.
The billion-year unit highlights the grandeur and incredible timescales involved in geological processes, aiding in deeper intellectual engagement with Earth's ancient history.

Comparative Analysis

Comparative analysis in the context of geological time involves evaluation and comparison of different time periods. This is essential for understanding which periods were longer or more significant in scale. The initial step is translating all time values into a common unit.
For instance, by converting years and million years into million years; and million years and billion years into billion years, it becomes much easier to determine which period is greater and by how much. Take, for example, 0.1 billion years being equal to 100 million years, showing a drastic difference when compared to just 1 million year.
Such comparisons not only help in academic calculations but also provide insights into geological timelines, assisting us in comprehending the vast stretches over which Earth's transformations occur.