Scientific notation is necessary for others to understand what equations we are talking about, for example, let's do an equation: 4 * 10^4, this is a scientific notation, as it is saying 4 times 10 to the power of 4 (10x10x10x10) and thus 4 * 10^4 is equal to 40,000, as you are 40 x 10 x 10 x 10.
How to do this equation is first multiply the 4 x 10 first, so that makes 40, then you multiply 40 x 10 x 10 x 10
For another example: 6 * 10^5, same thing here, 6 times 10 first makes 60, then you multiply 60 x 10 x 10 x 10 x 10, which makes 600,000.
Now it gets a little bit tough to understand with decimals: 3.102 * 10^2, to explain this, to multiply decimals it is easier to do a different equation, here's my explanation: first you convert the 10^2 to 100s aka 3.102 x 100, since 10x10 (10^2) is equal to 100,
now we have 3.102 * 100, now we just move the decimal twice to the right, or 3.012 + 100 = 301.2.
Notice how the 3.012 moved right twice? It's because when you add 10s to a decimal you move the decimal to the right.
1.75 x 10^-3 would move it to the left, and it would look like this 0.00175.
Now for multi-number multiplication, let's take (1.45 * 10^8) * (9.2 * 10^-12) * (3,01 * 10^-5)
now since this is multiplication, it doesn't matter what order we do these in, so to make it easier we can do it like 1.45 * 9.2 * 3.01, and then 10^8 +10^-12 + 10^-5.
Now do the powers first, 8 + -12 - 5 = -9 so -9 power, now 1.45 * 9.2 * 3.01 = 40.1534^-9, but this is not official scientific notation, to make it a correct notation you
must put 40.1534 to be equal to one and less than ten.
The proper way to write this is 4.01534 * 10 * 10^1 because you are moving the decimal to the right, as it is making the
notation into a single digit (4), and then you add the ^1 to the ^-9 to get
4.01534 * 10^-8
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