Rewrite the following number in scientific notation:

To write a number in scientific notation, we need to write it as a decimal times a certain power of ten. The decimal should be after the one's place. This means that ours should generally look like the following:

The next step is to determine the number of decimal places we had to move our decimal. This will tell us which power to raise our ten to

To go from

We had to move our decimal point 9 places. This means that our "n" will be nine.

A number in scientific notation takes the form

,

where either or and is an integer.

In the number

does not fit the criteria, since . does fit the criteria, since is an integer.

To pattern uses the formula .

Give the expanded form of the following scientific notation.

To expand this, we need to move the decimal point. Because our exponent is positive, we will be moving it 7 spaces to the right.

In order to do so, we need to add a couple zeros

So, our answer is

Scientific notation is written in the form .

In this equation, to go from standard to scientific notation, the decimal is shifted four places to the left.

Understanding this sequence takes a quick eye, so to speak. Notice this interesting fact. You can rewrite the sequence as follows:

That is a rather simple sequence if you think of it. The best clue to help you see it will likely be the transition between and . These are the numbers that will most like stand out as a square and a cube. Based on this data, you can reasonably guess that the next number in the sequence is or .

Recall that in an arithmetic sequence, we will be adding or subtracting the same number to get each successive term.

We can tell that the terms are decreasing by each time. Thus, we can make a table to figure out the tenth term.

The tenth term is .

The rules of scientific notation are simple. A number is being converted into a format where it's a decimal between 1 and just below 10 (9.9999999...) accompanied by an exponent. The exponent represents how many times to the decimal must move to the left or to the right to become the original number again. Scientific notation does not change the value of the number, but merely provide number in an easier to look at way. If the decimal must move to the right in order to achieve the original number, it will be represented by a positive exponent. If the decimal must move to the left, it will be represented by a negative exponent.

For this example, ,

we first write how this number would be if it were in decimal form (between 1 and just shy of 10).

This would be :

Now we must count how many times we had to move the decimal over to achieve this decimal. (Remember where the decimal is in the original number.) We can see that the decimal had to move times. With the decimal placed between the and , we see that if we wanted to go back to the original number (), we would have to move the decimal to the left. This means a negative exponent. Therefore, the answer would be:

Give the expanded form of the following scientific notation.

To expand this, we need to move the decimal point. Because our exponent is positive, we will be moving it 7 spaces to the right.

In order to do so, we need to add a couple zeros

So, our answer is

The rules of scientific notation are simple. A number is being converted into a format where it's a decimal between 1 and just below 10 (9.9999999...) accompanied by an exponent. The exponent represents how many times to the decimal must move to the left or to the right to become the original number again. Scientific notation does not change the value of the number, but merely provide number in an easier to look at way. If the decimal must move to the right in order to achieve the original number, it will be represented by a positive exponent. If the decimal must move to the left, it will be represented by a negative exponent.

For this example, ,

we first write how this number would be if it were in decimal form (between 1 and just shy of 10).

This would be :

Now we must count how many times we had to move the decimal over to achieve this decimal. (Imagine the decimal is after the last digit in the original number.) We can see that the decimal had to move times. With the decimal placed between the first two digits, we see that if we wanted to go back to the original number (), we would have to move the decimal to the right. This means a positive exponent. Therefore, the answer would be: