Question

earth is approximately 5×10^9 years old. for which of these ages could this be an approximation? select all that apply. a. 4.26×10^9 years b. 49,000,000,000 years c. 4.829999999×10^9 years d. 4,962,000,000 years e. 4,581,600,000 years

Explanation:

Step1: Recall approximation concept

Approximation means a value is close to the given value. We'll check how close each option is to $5\times 10^{9}$.

Step2: Analyze option A

$4.26\times 10^{9}$ is close to $5\times 10^{9}$ as the difference is $(5 - 4.26)\times 10^{9}=0.74\times 10^{9} = 740000000$.

Step3: Analyze option B

$49000000000 = 4.9\times 10^{10}$. The difference from $5\times 10^{9}$ is $4.9\times 10^{10}-5\times 10^{9}=49\times 10^{9}-5\times 10^{9}=44\times 10^{9}$, so it's not a good approximation.

Step4: Analyze option C

$4.829999999\times 10^{9}$ is close to $5\times 10^{9}$ with a small difference of $(5 - 4.829999999)\times 10^{9}=0.170000001\times 10^{9}=17000000.1$.

Step5: Analyze option D

$4962000000 = 4.962\times 10^{9}$. The difference from $5\times 10^{9}$ is $(5 - 4.962)\times 10^{9}=0.038\times 10^{9}=38000000$, so it's close.

Step6: Analyze option E

$4581600000 = 4.5816\times 10^{9}$. The difference from $5\times 10^{9}$ is $(5 - 4.5816)\times 10^{9}=0.4184\times 10^{9}=418400000$, so it's close.

Answer:

A. $4.26\times 10^{9}$ years, C. $4.829999999\times 10^{9}$ years, D. $4962000000$ years, E. $4581600000$ years