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Scientific Notation

Scientific Notation

Author: Abigail Baker
Description:
  1. Demonstrate how to write a number in scientific notation.

  2. Show examples of how to add/subtract/multiply/divide numbers written in scientific notation.

This packet should help a learner seeking to represent numbers in scientific notation.

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Tutorial

Changing a Number into Scientific Notation

NOTES: Expressing numbers in scientific notation

GENERAL RULES FOR CHANGING A NUMBER INTO SCIENTIFIC NOTATION

  1. Change the number so it only has one nonzero digit in front of a decimal point. It should be a number between 1 and 10.
  2. Determine how many steps and in what direction the new number needs to move the decimal to get back to the original number.
    • The number of steps will be the exponent.
    • If you move the decimal to the right, the exponent will be positive.
    • If you move the decimal to the left, the exponent will be negative.
  3. Write your new number with 10 raised to the exponent.

EXAMPLE 1:

Express the number 1,642,000 in scientific notation.

1,642,000 becomes 1.642000

For 1.642000, the decimal needs to move 6 times to the right to get back to the original number.

In scientific notation,

1,642,000 is 1.642000 x 106 or 1.642 x 106

EXAMPLE 2:

Express the number 0.00000000520 in scientific notation.

0.00000000520 becomes 5.20

For 5.20, the decimal needs to move 9 times to the left to get back to the original number.

In scientific notation,

0.00000000520 is 5.20 x 10-9

 

NOTES: Addition and Subtracting Numbers in Scientific Notation

RULES FOR ADDITION AND SUBTRACTION

  1. Change the numbers so that the powers of 10 are the same.
  2. Add/Subtract the coefficients (the numbers that are multiplied by the power of 10).
  3. The power of 10 is the same as what you
  4. Express the answer in the correct scientific notation.

Addition Example

1.02 x 1012 + 3.01 x 1013 = ?

1.02 x 1012 + 30.1 x 1012 (you could also change both to 1013)

1.02 + 30.1 = 31.12

Answer: 31.12 x 1012

Correct scientific notation: 3.112 x 1013

Subtraction Example

1.2 x 10-3 - 2.5 x 10-5 = ?

1.2 x 10-3 - 0.025 x 10-3

1.2 - 0.025 = 1.175

Answer and Correct scientific notation: 1.175 x 10-3

NOTES: Multiplying and Dividing Numbers in Scientific Notation

RULES FOR MULTIPLYING

  1. Multiply the coefficients (numbers multiplied by the power of 10).
  2. For the power of 10, add the exponents for the numbers you are multiplying.

Multiplication Example

6.02 x 1023 x 2.15 x 10-5 = ?

(6.02 x 2.15) x (1023 x 10-5) = 12.943 x 10 23+ (-5)

Answer: 12.943 x 1018

Correct scientific notation: 1.2943 x 1019

 

RULES FOR DIVIDING

  1. Divide the coefficients (numbers multiplied by the power of 10).
  2. For the power of 10, subtract the exponents for the numbers you are multiplying.

Division Example

6.02 x 1023 / 2.15 x 10-5 = ?

(6.02 / 2.15) x (1023 / 10-5) = 12.943 x 10 23 - (-5)

Answer and Correct scientific notation: 2.8 x 1028