Question

How do you express the product of `(35,000)(.00046)` in scientific notation?

Answer 1

First you write both numbers in scientific notation

`35000=3.5*10^4`
because you have to move the decimal point 4 places to the left to leave one non-zero digit in front of the decimal point

`0.00046=4.6*10^-4`
decimal point 4 to the right to get one one-zero digit in front of the decimal point (remember: to the right means negative `10`-power)

Now you multiply the numbers and add the `10`powers:

`3.5*4.6=16.1` and `4+(-4)=0`

So the initial answer is `16.1*10^0`
But we now have two non-zero numbers before the decimal point,so:
`16.1*10^0=1.61*10^1` (move one to the left)