# GED Math : Scientific Notation

## Example Questions

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### Example Question #1 : Scientific Notation

Write the following number in scientific notation:

Explanation:

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.

### Example Question #2 : Scientific Notation

Write the following number in standard notation:

Explanation:

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:

### Example Question #1 : Scientific Notation

Write the following number in scientific notation.

Explanation:

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 .

### Example Question #1 : Scientific Notation

Write the following number in scientific notation.

Explanation:

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 .

### Example Question #2 : Scientific Notation

Multiply and express the product in scientific notation:

Do not use a calculator.

Explanation:

Apply the exponent properties:

or, more correctly, .

### Example Question #6 : Scientific Notation

Divide, and express the quotient in scientific notation.

Do not use a calculator.

Explanation:

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, .

### Example Question #7 : Scientific Notation

Divide, and express the quotient in scientific notation.

Do not use a calculator.

Explanation:

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

or .

### Example Question #8 : Scientific Notation

Which of the following values is equivalent to,

?

Explanation:

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

### Example Question #2 : Scientific Notation

How many significant figures are present in the scientific notation form?

Explanation:

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.

### Example Question #4 : Scientific Notation

Which of the following numbers can be written in scientific notation as  ?