To find the approximate percentage of geologic time that humans have existed on Earth since its origin, we need to follow these steps:
1. Identify the relevant time periods:
- Years humans have existed: Approximately 200,000 years.
- Age of the Earth: Approximately 4.54 billion years (which is 4.54 × 10^9 years).
2. Set up the percentage calculation formula:
[tex]\[
\text{Percentage} = \left( \frac{\text{Years humans have existed}}{\text{Age of the Earth}} \right) \times 100
\][/tex]
3. Plug in the values:
[tex]\[
\text{Percentage} = \left( \frac{200,000}{4.54 \times 10^9} \right) \times 100
\][/tex]
4. Perform the calculations:
- First, divide 200,000 by 4.54 billion.
[tex]\[
\frac{200,000}{4.54 \times 10^9} = \frac{200,000}{4,540,000,000} \approx 4.4052863436 \times 10^{-5}
\][/tex]
- Then, multiply by 100 to convert the fraction to a percentage.
[tex]\[
4.4052863436 \times 10^{-5} \times 100 \approx 0.0044052863436 \%
\][/tex]
5. Round the result to make it more comprehensible (if necessary):
- The result [tex]\(0.0044052863436\%\)[/tex] is already very small and accurate enough for our purposes.
6. Compare the calculated percentage with the given options:
- Less than 1% (A)
- 1.8% (B)
- 11.8% (C)
- More than 25% (D)
From our calculation, we can see that 0.0044052863436% is significantly less than 1%.
Therefore, the approximate percentage of geologic time that humans have existed on Earth is:
A) less than 1%
