Section: Mathematical Reasoning

2)

Simplify the following using scientific notation: 

^{(83.9 x 1012)(2.87 x 10-3)}/_{3.76 x 10²}

1. 0.6404 x 10^-1
2. 6.404 x 10¹⁸
3. 64.04 x 10^-1
4. 6.404069148 x 10⁸

Using scientific notation, this problem would have three main steps.

First, you would multiply the numbers in the numerator (83.9 x 2.87) and divide them by the number in the denominator (3.76). Answer is approximately 64.04069148.

Secondly, you would divide the exponents of the numerator and denominator (12 + (-3))-2. Answer is 7 (or 10⁷). Now multiply the two together and you get 64.04069148 x 10⁷.

Finally, move your decimal space one to the left and add a one to your exponent to get 6.404069148 x 10⁸.

This ensures that the answer meets the demands of scientific notation, which is a number should be greater than or equal to 1 and less than 10 times 10 raised to some power. Option 4 is the only one that meets the criteria.