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.