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5 votes
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)

User Reimius
by
6.8k points

1 Answer

5 votes

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.

User The Vinh Luong
by
6.6k points
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