This can be most easily solved by writing the expression in fraction form, then applying the rules of exponents as follows:

,

or, more correctly written, .

This can be most easily solved by writing the expression in fraction form, then applying the rules of exponents as follows:

or .

When multiplying a decimal using base 10 with a negative exponent, the method is to move the decimal point to the left the amount of spaces which is indicated by the exponent.  In this example, you will move the decimal point four spaces to the left because the exponent is . Because there is only one decimal place to the left of the decimal indicated by the whole number 3, you will need to annex or add three zeroes to the left of the three as place holders, thus making the correct answer  

The significant figures will only count the number .  

All non-zero digits are significant figures, and the values after the decimal place are also considered as significant digits.

Do NOT expand the term to  or the significant digits will be lost.

The answer is:  

To convert  to standard notation, first note that

Multiply this by 5.7:

,

the correct choice.

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