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Introduction to Scientific Notation: Efficiently Writing and Calculating Very Large and Very Small Numbers

Learn how to write numbers using scientific notation, a shorthand method using powers of 10, improving efficiency and accuracy in calculations with large and small values. Practice recognizing and converting numbers from scientific notation to standard form and vice versa. Also, explore multiplying and dividing numbers in scientific notation.

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Introduction to Scientific Notation: Efficiently Writing and Calculating Very Large and Very Small Numbers

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  1. Warmup • Space tourism is a multibillion dollar industry. For a price of $20 million, a civilian can travel on a rocket or space shuttle and visit the International Space Station for a week. • What would $20 million look like when written out? • What would you have to multiply $2 by to get to $20 million? • How can you write 10,000,000 as a power of 10?

  2. Scientific Notation Writing a number in scientific notation improves efficiency and accuracy of various calculations involving VERY LARGE and VERY SMALL numbers. Lesson 7-2

  3. Scientific notation is a shorthand way to write numbers using powers of 10. Examples: 8.3 x 105 4.12 x 1022 7.1 x 10-5 Standard notation is a number written with place values. Examples: 1529.5 0.085 Vocabulary

  4. 1) 0.23 x 10-3 2) 2.3 x 107 3) 9.3 x 1009 Problem 1: Recognizing Scientific Notation Is the number written in scientific notation? If not, explain. • Conditions: • 1st factor is between 1 and 9 • 2nd factor is a power of 10

  5. Got it? 4) 53 x 104 5) 3.42 x 10-7 6) 0.35 x 100 Is the number written in scientific notation? If not, explain.

  6. Scientific Form  Standard Form The exponent tells you how many places to move the decimal point. If there is a positive exponent, move the decimal place to the ________. If an exponent is positive, a number gets ____________. If there is a negative exponent, move the decimal place to the _________. If an exponent is negative, a number gets ______________. Concept

  7. Scientific Notation to Standard Form 1. Express 6.49 × 105 in standard form. Example 2A

  8. Scientific Notation to Standard Form 2. Express 1.8 × 10–2 in standard form. Example 2B

  9. 3. Express 3.16 × 10–2 in standard notation. Example 2A

  10. 4. Express 7.61 × 103 in standard notation. Example 2B

  11. Standard Form  Scientific Form • 1) Move the decimal after the first whole number • (1, 2, 3, 4, 5, 6, 7, 8, 9). • 2) Add your multiplication sign and base (x 10) • 3) The number of moves between the original and the new decimal place will be the exponent. • If the original number is greater than one, the exponent will be ___________. • If the original number is less than one, the exponent will be ___________. Concept

  12. Standard Form to Scientific Notation 1. Express 4,062,000,000,000 in scientific notation. Example 1A

  13. Standard Form to Scientific Notation 2. Express 0.000000823 in scientific notation. Example 1B

  14. 3. Express 458,000,000 in scientific notation. Example 1A

  15. 4. Express 0.0000452 in scientific notation. Example 1B

  16. Multiply and Dividing in Scientific Notation • When you multiply in scientific notation, just multiply the first factor and _________ the exponents. • When you divide in scientific notation, just divide the first factor and _________ the exponents.

  17. Multiply with Scientific Notation 1. Evaluate (5 × 10–6)(2.3 × 1012). Express the result in both scientific notation and standard form. Example 3

  18. 2. Evaluate . Express the result in both scientific notation and standard form. Divide with Scientific Notation Example 4

  19. 3. Evaluate (8 × 105)(2.1 × 10–3). Express the result in both scientific notation and standard form. Example 3

  20. 4. Evaluate Express the result in bothscientific notation and standard form. Example 4

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