Question

Standard Notation and Scientific Notation Tutorial
Creator of Tutorial: LegendarySadist

Answer 1

Tutorial on Standard Notation and Scientific Notation. I'm making this because I find it hard to really explain the concept of moving the decimal to someone else in a short post.

Anyways, let's get onto it. The basic concept behind standard notation and scientific notation is multiplying and dividing by 10. Multiplying by 10 is a very clean process, and I'm sure we all understand it well, but I want to go over it in a different perspective for the tutorial. We usually view a number just as is, but it can also be represented with an infinite number of zeros on each side of it.

For example, \(\large \sf 50=0000000050.000000000000\) with the zeros going on forever on both sides. If we multiply 50 by 10, we normally would just put another zero onto the end of 50, but that could also be represented by moving the decimal over to the right once. \(\large \sf 00050.000 \huge \rightarrow \large 000500.00\) which will still get us 500.

Now we don't really need to use an infinite number of zeros every time, as long as we understand the concept. So for an example problem, if we have \(\large \sf 7.384\) and we multiply that be 10 we would move the decimal over once to get \(\large \sf 73.84\)

And this process works the same way when we divide by 10 instead of multiplying. The difference is that instead of moving the decimal one to the right, we move it to the left. So \(\large \sf 60 \div 10\) is the same as moving the decimal \(\large \sf 60.0\) once to the left, giving us now \(\large \sf 6.00=6\)

Now that we understand multiplying/diving by 10, we can see how this applies to standard notation and scientific notation. Standard notation is how we write "normal" numbers. It refers to writing them like 5, 7.32, 300, etc. On the other hand, scientific notation means bringing the number to a value under 10, and then multiplying it by \(\large \sf 10^x\) to make it represent the number as it was in standard notation. It is most commonly used to convey very large numbers in a smaller format.

It is much easier to see it instead. For example 500 in scientific notation would be \[\large \sf 500 \rightarrow 5 \times 100 \rightarrow 5 \times 10^{2}\] The easiest way to convert to scientific notation is to make use of multiplying by tens. Going back to the 500 example, we would look at it like \(\large \sf 500.0\) and we would count the number of zeros needed to bring the 5 so that it is right next to the decimal. In this case it would be 2 spaces, so we would get \(\large \sf 5 \times 10^{2}\) . You could repeat this process to see that 5000.0 would 3 spaces, 50000.0 would have 4 spaces, and so on. For x spaces away from the decimal it is \(\large \sf 10^{x}\) in scientific notation.

We will use a similar process for decimal values. However, we will represent it as a division of 10 instead. So if we have 0.00425, we would see how many places we have to move the 4 to get in front of the decimal. In this case, it would take 3 spaces to get in front of the decimal, leaving us with 4.25, which we would multiply by \(\large \sf 10^{-x}\) with x being the number of spaces needed to get the 4 before the decimal. So our end result would be \[\large \sf 0.00425 \rightarrow 4.25 \times 10^{-3}\]
The last part of the tutorial is converting scientific notation back to standard notation. This is a fairly simple process. You just move the decimal over to the right or left x amounts of time depending on whether the exponent is positive or negative. So \(\large \sf 7.3 \times 10^{3}\) would be \(\large \sf 7.3000\) with the decimal moved 3 times to the right making the result be \(\large \sf 7300.0\).

You can apply the same process for \(\large \sf 6.22 \times 10^{-4}\) with the difference being you will move the decimal to the left. So we would have 00006.22 which we would move the decimal 4 times to the left giving us the result of \[\large \sf 00006.22 \times 10^{-4} \rightarrow 0.000622\]

And that concludes my tutorial about standard notation and scientific notation.

Answer 2

UM, OKAY?

Answer 3

MATHMATICS NOTATION.

Answer 4

If your question is answered, please close it. Thank you.

Answer 5

thanks