Question

How do I do scientific notation word problems?

Answer 1

Scientific notation is just a convenient way of shortening long numbers so they're easier to read and is written in the form of
`x*10^(n)` where x is an integer or a decimal, and n is an integer.

If 10 is being raised to a positive power, that's the number of places you move the decimal over to the RIGHT. For example
`4.5*10^(3)` could also be written as 4500 (or 4500.0 so you can see what I mean by "moving the decimal over"). For negative exponents, the decimal is moved over that many spaces to the LEFT. For example,
`6.7*10^(-2)` could also be written as .067 (or 0.067. See how the decimal place was moved over two places to the left this time). And remember, anything to the power of 0 is 1. So
`8.2*10^(0)` is the same thing as
`8.2*1`, or simply 8.2.

To do addition or subtraction on scientifically notated numbers, ensure that both numbers are being multiplied by 10 to the same power. If not, convert one of them using the above information. Now, just add the two numbers being multiplied by
`10^(n)` and your answer will be (their sum)
`*10^(n)`.

To do multiplication on scientifically notated numbers, just multiply the two numbers out front and add the two powers that 10 is being raised to. For example,
`(4.1*10^(5))*(3.2*10^(4)) = (4.1*3.2)*10^(5+4)` which simplifies to
`13.12*10^(9)`.

To do division on scientifically notated numbers, this time DIVIDE the two numbers out front and SUBTRACT the exponents of 10.