Some of the way scientific notation is written here is a little strange. Be sure to click here for more explanation.  Be sure to SUBMIT when you are done!! (This is new, will send me the score)

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More Explanation:

You live in a digital age. You need to know how computers do exponents.

Computer languages often express a power using the ^ symbol. 5 squared is 5^2. 4 cubed is 4^3. Scientific notation of 24000 is 2.4 x 10^3 and 0.005 is 5 x 10 ^ -3.

Another way a computer (or calculator) may express scientific notation is with an e. 360 would be 3.6e+2, 7000 would be 7e+3, 0.00059 would be 5.9e-4

One particular problem that might give you trouble is "A microscopic circle has a radius that is 2 x 10^-7 meters. What is its area in square meters?" To do this it's (2x10^-7)(2x10^-7)(3.14) which is 12.56 x 10^-14. This is correct but not in scientific notation. It should be converted to 1.256x10^-13.

Another example per Lonny's request

A tiny rectangle has a side of length 4x10^-15 feet and a width of 6x10^-4 feet. What is its area in square feet? Area is length times width so (4x10^-15)(6x10-4) is 24 x 10^-19. This is correct but it needs to be 2.4 as the coefficient to be in scientific notation. 24 is 2.4 x 10^1 times the existing 10^-19 and you get 2.4 x 10^-18

And one more: A gargantuan right prism with a rectangular base (a.k.a. a box!) has a side of length 7x10^18 feet, a width of 8x10^17 feet, and a height of 9x10^7 feet. What is its volume in cubic feet? Volume is area of the base times the height so (7x10^18)(8x10^17)(9x10^7) which is 504 x 10^42. Once again the correct answer but not in scientific notation. 504 is 5.04 x 10^2. We multiply this times the 10^42 and get 5.04 x 10^44.


Area for rectangles is simply how many squares fit in the space. If it's 3 units long and 4 units high, that's 4 stacks of 3 squares or 12 (3x4) square units

Area for a circle is pi times the radius squared. So a circle with the radius of 3 units has an area of 3x3x3.14 units. (I could also tell you diameter in which case you'd have to chop it in half first to get radius)

Volume is how many cubes of a certain size fit inside a solid. A box that is 3x4 on the bottom has 12 cubes that will fit on "the first floor". If the box is 10 high, then there are 120 (3x4x10) cubic units inside the box

Figuring out the number of cubes inside of a sphere (a ball) would be difficult. However someone figured out the formula for this is 4/3pi r cubed. So if a sphere had a radius of 10, the volume would be 4 / 3 x 3.14 x 10 x 10 x 10 or approximately 4186.67 cubic units