Dinosaurs have been extinct for about 6.5 x 10^(7) years, while Neanderthals have been extinct for about 3.0 x 10^(4) years. About how many times longer have dinosaurs been extinct than Neanderthals?

Question

A. 1,000 times longer

B. 2,000 times longer

C. 10,000 times longer

D. 20,000 times longer

Answer 1

To find out how many times longer dinosaurs have been extinct than Neanderthals, we can divide the time since their extinction:

1. The time dinosaurs have been extinct: \(6.5 \times 10^{7}\) years
2. The time Neanderthals have been extinct: \(3.0 \times 10^{4}\) years

Now, we can perform the division:

\[ \frac{6.5 \times 10^{7}}{3.0 \times 10^{4}} = \frac{6.5}{3.0} \times \frac{10^{7}}{10^{4}} \] Calculating the parts separately:

1. \( \frac{6.5}{3.0} \approx 2.1667 \)
2. \( \frac{10^{7}}{10^{4}} = 10^{(7-4)} = 10^{3} = 1000 \)

Now, multiply these results:

\[ 2.1667 \times 1000 \approx 2166.7 \]

Rounding this to significant figures, we find that dinosaurs have been extinct about 2,000 times longer than Neanderthals.

The closest answer to this result is:

B. 2,000 times longer.