Question

the oldest rocks on earth are about 4 10^9 years old. for which of these ages could this be an approximation? select all that apply. a. 3.849999999 10^9 years b. 4,149,000,000 years c. 3,862,100,000 years d. 0.000000004 years e. 3.45 * 10^9 years

Explanation:

Step1: Convert all options to scientific - notation if needed

• Option A: $3.849999999\times 10^{9}$ is already in scientific - notation.
• Option B: $4149000000 = 4.149\times 10^{9}$
• Option C: $3862100000 = 3.8621\times 10^{9}$
• Option D: $0.000000004=4\times 10^{- 9}$
• Option E: $3.45\times 10^{9}$ is already in scientific - notation.

Step2: Determine which values are close to $4\times 10^{9}$

• We consider values that are relatively close to $4\times 10^{9}$.
• For Option A: $\vert4\times 10^{9}-3.849999999\times 10^{9}\vert=(4 - 3.849999999)\times 10^{9}=0.150000001\times 10^{9}$
• For Option B: $\vert4\times 10^{9}-4.149\times 10^{9}\vert=(4.149 - 4)\times 10^{9}=0.149\times 10^{9}$
• For Option C: $\vert4\times 10^{9}-3.8621\times 10^{9}\vert=(4 - 3.8621)\times 10^{9}=0.1379\times 10^{9}$
• For Option D: $\vert4\times 10^{9}-4\times 10^{-9}\vert\approx4\times 10^{9}$ (since $4\times 10^{-9}$ is extremely small compared to $4\times 10^{9}$)
• For Option E: $\vert4\times 10^{9}-3.45\times 10^{9}\vert=(4 - 3.45)\times 10^{9}=0.55\times 10^{9}$

Options A, B, C, and E are relatively close to $4\times 10^{9}$.

Answer:

A. $3.849999999\times 10^{9}$ years, B. $4149000000$ years, C. $3862100000$ years, E. $3.45\times 10^{9}$ years