Perhaps the easiest way to do this is to consider the number  when it is taken out of scientific notation.  Based on the power of  provided, you know that you must move the decimal point to the right by  spaces.  This gives you:

Now, you need to think through all of the options in a similar way to figure out which one matches.  The only one that works is .

Remember that a negative exponent like this will require you to move the decimal point to the left—two places in this case.  Thus, it gives you:

Which of the following is the equivalent to the decimal ?

To change a decimal to scientfic notation, first count the number of places from the decimal to the digit you want as the one's digit.

In this case, we want our scientific notation to begin with 6.3, that means that we need to move the decimal point seven places:

Furthermore, we are moving 7 spaces to the left. Therefore, our exponent in scientific notation must be negative 7. 

Thus, our answer is:

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.

Rewrite the following decimal in scientific notation with 3 significant digits.

Scientific notation follows the format of

Where n is a decimal and m is the number of digits the decimal moves over.

In this case, we want to have n be 6.16, because this will give us 3 significant digits. 

In order to get to 6.16, we need to move the decimal place how many places?

5 places! Moreover, 5 places to the right. This means that our m=-5

General rule of thumb: If your decimal is smaller than your scientific notation, then your exponent will be negative. If your starting number is greater than your scientific notation, your exponent will be positive.

So, our answer is:

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

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.

Start by multiplying the two terms.

Next, recall that in scientific notation, the digits must be a number less than  that is multiplied by a power of . Thus, we can rewrite  as  in scientific notation.

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:

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 the decimal is between  and  in the original number.) We can see that the decimal had to move  time. 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 right. This means a positive exponent. Therefore, the answer would be:

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 the decimal is between  and  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 right. This means a positive exponent. Therefore, the answer would be: