Question

Problem B: Raising a number in Scientific Notation to a Power
According to Guinness World Records, the largest Rubik's cube in the world is 2.022*10^2 centimeters on each
side. What is the volume of this cube? Write your answer in scientific notation. (v=s^3)

Answer 1

Answer: Roughly 8.267*10^6 cubic centimeters

The more accurate answer is 8.266914648*10^6 cubic centimeters

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Work Shown:

$s = 2.022*10^2\\\\v = s^3\\\\v = (2.022*10^2)^3\\\\v = (2.022)^3*(10^2)^3\\\\v = 8.266914648*10^{2*3}\\\\v = 8.266914648*10^6\\\\v \approx 8.267*10^6$

I rounded to three decimal places because the 2.022 is to three decimal places. Round however you need. Or you can choose to leave the number unrounded.

The number 8.267*10^6 is 8,267,000 which is a little over 8.2 million.

The units for the volume are in cubic centimeters, which we can abbreviate as cm^3 or $\text{cm}^3$

Note that the value $8.267*10^6$ is in the form $A*10^b$ where $0 \le A < 10$, which means this number is in scientific notation form.