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Scientific Notation

Operations Using Exponents

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Scientists and engineers often work with very large or very small numbers, which are more easily expressed in exponential form or scientific notation. You write a very large number in scientific notation by moving the decimal point to the left until only one digit remains to the left. The number of moves of the decimal point gives you the exponent. For example:

3,454,000 =

3.454 x 106

For very small numbers, you move the decimal point to the right until only one digit remains to the left of the decimal point. The number of moves to the right gives you a negative exponent:

0.0000005234 =

5.234 x 10-7

Addition Example Using Scientific Notation

Addition and subtraction problems are handled the same way.

  1. Write the numbers to be added or subtracted in scientific notation.
  2. Add or subtract the first part of the numbers, leaving the exponent portion unchanged.
  3. Make sure your final answer is written in scientific notation.
(1.1 x 103) + (2.1 x 103) =

3.2 x 103

Subtraction Example Using Scientific Notation

(5.3 x 10-4) - (2.2 x 10-4) =

3.1 x 10-4

Multiplication Example Using Scientific Notation

You do not have to write numbers to be multiplied and divided so that they have the same exponents. You can multiply the first numbers in each expression and add the exponents of 10 for multiplication problems.

(2.3 x 105)(5.0 x 10-12) =

When you multiply 2.3 and 5.3 you get 11.5. When you add the exponents you get 10-7. At this point your answer is:

11.5 x 10-7

You want to express your answer in scientific notation, which has only one digit to the left of the decimal point, so the answer should be rewritten as:

1.15 x 10-6

Division Example Using Scientific Notation

In division, you subtract the exponents of 10.

(2.1 x 10-2) / (7.0 x 10-3) =

0.3 x 101 =

3

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