How do you evaluate `0.028\times ( 3.4\times 10^ { 4} )`?

-Begin with the brackets. Within the brackets, there is an exponent. Evaluate. It should give 10,000.

-Then multiply this number by 3.4 because it's in the brackets. You should get 34,000.

-Finish by multiplying this by 0.028. You should get 952

Lets get rid of the decimals for now and then put them back at the end

`3.4` is the same as `34xx1/10`

So `3.4xx10^4` is the same as `34xx1/10xx10^4 color(white)("dd") =color(white)("dd") 34xx10^3`

`0.028` is the same as `28xx1/1000 = 28xx1/10^3`
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`color(blue)("Putting it all together")`

`28xx1/10^3xx34xx10^3`

`28xx34xx10^3/10^3`

`28xx34 = 952`

Choosing to put this into the same format as in part of the question `(3.4xx10^4)` we have:

`952 ->9.52xx10^2`

`0.028 * (3.4 * 10^4)` Given Equation

First off, lets start with finding the value inside the brackets.
`3.4 * 10^4` In a way, this is just scientific notation, meaning that the number just by looking at it would be `34,000`.

However, if you are not familiar with scientific equation, you can first look at `10^4`. Well, what is `10 * 10 * 10 * 10`? It would be `10,000`.

Now that you have that part, we can continue looking inside the brackets. Giving us `3.4 * 10,000`. The way I would solve this is by, looking at the ONLY numbers that are not `0`.

So, really we are looking at `3.4 * 1`, which is `3.4`. Now we add the left over zeros, since `10,000` has a total of `4` zeros, add `4` zeros to `3.4`.

So `(3.4 * 10^4) = 34,000`. Great! Now to solve the rest.

`0.028 * 34,000` Is now leftover. Could solve this like a regular multiplication problem.

`34 * 28 = 952`, I would add the `3` zeros from `34,000`, however since `0.028` has `3` numbers behind the decimal point, that would cancel everything out. Making the answer be `952`.