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Scientific Notation: Converting, Adding, Subtracting, Multiplying, and Dividing

Learn how to convert numbers into scientific notation, perform arithmetic operations, and simplify the results. Practice examples included.

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Scientific Notation: Converting, Adding, Subtracting, Multiplying, and Dividing

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  1. Warm up 1. If you invest $1,000 at 7% for 2 years. How much will you have after two years if it compounds annually? $1144.90 2. How much money should I save in an account paying 10% interest compounded yearly if I want to have $484 in 2 years? $400

  2. Scientific Notation TSWBAT: • Write numbers in scientific notation • Write numbers in standard form from scientific notation • Add and Subtract numbers in Scientific Notation • Multiply and Divide numbers in Scientific Notation

  3. We use scientific notation as a shorter way of writing really big numbers (or really tiny numbers). • You have over 3,750,000,000,000,000,000 genes in your body. • The influenza virus is about 0.00000001 meters in diameter.

  4. What does Scientific Notation look like? a number between 1 and less than 10 x a power of 10 Rules for converting standard form to Scientific Notation 1. Move the decimal to the right of the first nonzero number 2. Count the # of places the decimal moved (that is the exponent on 10) Original number > 1 then positive exponent on the 10 Original number < 1 then negative exponent on the 10

  5. Let’s work together! 1. 123,000,000,000,000 2. 0.000000000236

  6. You Try! 1. 2. • 7,080,000,000,000 • 0.00000001256

  7. To convert to standard form • Move the decimal the number of places of the power of 10. • Move to the right for positive exponents • Move to the left for negative exponents.

  8. + Adding and Subtracting numbers in Scientific Notation To add or subtract numbers in scientific notation must have the same power of 10! Add/Subtract the numbers. Remember to line the decimals up; the power of 10 will remain the same in your answer.

  9. + What happens when the number is greater than 10? Make sure that you put your answer into scientific notation; that number must be at least 1 but less than 10 Remember to change the power of 10 too.

  10. In Summary. . . • Scientific notation is used to _____________________. • To add or subtract numbers in scientific notation ______________ ____________________________. • After adding or subtracting numbers in scientific notation you need to check and make sure that they are in __________ still. Write really big/small numbers easier The powers of 10 MUST be the same. Line up the decimals, add/subtract and keep the power of 10. Scientific Notation

  11. Multiplication with Scientific Notation 4 Simple steps Step 1: Multiply the numerical portion as normal. Step 2: Multiply the powers of 10 using the exponent rules. Step 3: Put your answer together as a product of a number and a power of 10. Step 4: Check to make sure you don’t have to fix the answer.

  12. Ex. : • Step 1: Multiply 4.3 and 2 • Step 2: Multiply 102 and 108 • Step 3: Write the answer in Scientific Notation. Step 4: Is the answer in Scientific Notation? Yes

  13. Let’s look at another one… Multiply 4.2 and 3.8 together Multiply the powers of 10 together using exponent rules Write in Scientific Notation No Is the answer in Scientific Notation? Rewrite the answer in Scientific Notation

  14. Division with Scientific Notation • The same steps apply with division of scientific notation. • Step 1: Divide the numbers first. • Step 2: Divide the powers of 10 using exponent rules • Step 3: Put your answer together as a product of a number and a power of 10. • Step 4: Check that your answer is in scientific notation.

  15. Examples • Ex. 1: • Step 1: Divide the numerical portion. • Step 2: Simplify the power of 10 portion using exponent rules. • Step 3: Write in scientific Notation • Step 4: Check to make sure your answer is in scientific notation.

  16. One more time! Divide First divide 2.8 by 3.2 Now divide the powers of 10 using exponent rules Write in Scientific Notation Is this in Scientific Notation? No, it needs fixed!

  17. Your Turn Try these examples 1. 2. 3. 4. • Answers • 2.86 x 1017 • 9.6 x 10-10 • 3.2 x 10-4 • 1.31579 x 100

  18. In Summary. . . • When multiplying numbers in Scientific • Notation • ______________________________ • When dividing numbers in Scientific Notation • ________________________________ Multiply the numbers as normal and use exponent rules when multiplying the powers of 10. Divide the numbers as normal and use the exponent rules to divide the powers of 10

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