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Scientific Notation

This guide explores the essential concepts of scientific notation, focusing on how to represent numbers in this format and convert them back to decimal form. To express a number in scientific notation, move the decimal point until the resulting number is between 1 and 10, then multiply by a power of ten that corresponds to the decimal movement. The document provides examples such as converting 3.4690 to (3.4690 times 10^4) and transitioning back to decimal for numbers like (2.834 times 10^2).

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Scientific Notation

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  1. Scientific Notation

  2. Essential Question • How do I use scientific notation to represent numbers?

  3. How do we write numbers in Scientific Notation? • To put a number in scientific notation, first move the decimal to the right or left until the number is greater than 1, but less than 10. • Then write the power of 10 • By moving the decimal 3 places to the left, we really divided by 1000. So we have to multiply by 103 in order to represent the original number. • Example: 2 6 7 8 × 103

  4. Example 1 • Write in scientific notation. 3 4,6 9 0 = 3.4690 × 104

  5. Example 2 • Write in scientific notation. 0 0 3 9 = 3.9 × 10-2

  6. Example 3 • Write in scientific notation. 5,6 0 0,0 0 0,0 0 0 = 5.6 × 109

  7. Example 4 • Write in scientific notation. 0 0 0 0 7 2 2 = 7.22 × 10-4

  8. Writing in Decimal form • To change a number from scientific notation to decimal form just move the decimal. • + Exponent: move right • - Exponent: move left

  9. Example 5 • Write in decimal form. 2.834 × 102 = 2 8 3 4 = 283.4

  10. Example 6 • Write in decimal form. 4.9 × 105 4 9 0 0 0 0 = 490,000

  11. Example 7 • Write in decimal form. 7.8 × 10-1 = 7 8 = .78

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