Scientific Notation - GED Math

When calculating standard notation from scientific notation, if the exponent is negative, the decimal point must move that number of spaces to the left. If the exponent is positive, the decimal point must move that number of spaces to the right . In this problem, the exponent is negative, therefore we must move the decimal three places to the left:

A number that is wrtiten in scientific notation includes the number with a decimal point after the first number and , where is the number of times you need to move the decimal point.

So, if you write in scientific notation, it would be: , which is equivalent to . This shows that you need to move the decimal point two places to the right so it equals . Similarly, would be , which is equivalent , where you move the decimal point three places to the left.

becomes , which is equivalent . You would move the decimal point five places to the right to go back to .

A number that is wrtiten in scientific notation includes the number with a decimal point after the first number and , where is the number of times you need to move the decimal point.

So, if you write in scientific notation, it would be: , which is equivalent to . This shows that you need to move the decimal point two places to the right so it equals . Similarly, would be , which is equivalent , where you move the decimal point three places to the left.

becomes , which is equivalent . You would move the decimal point three places to the left to go back to .

To convert to standard notation, first note that

Multiply this by 5.7:

,

the correct choice.

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

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

or .

Apply the exponent properties:

or, more correctly, .

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, .

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:

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

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:

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. (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: