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Evaluate each expression. 1. 123  1,000 2. 123  1,000 3. 0.003  100 4. 0.003  100

Warm - Up. Evaluate each expression. 1. 123  1,000 2. 123  1,000 3. 0.003  100 4. 0.003  100 5. 10 4 6. 10 –4 7. 23 0. 123,000. 0.123. 0.3. 0.00003. 10,000. 0.0001. 1. Scientific Notation. Do you know your place?. 123456.54321. Label the place value of each digit

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Evaluate each expression. 1. 123  1,000 2. 123  1,000 3. 0.003  100 4. 0.003  100

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  1. Warm - Up Evaluate each expression. 1. 123  1,000 2. 123  1,000 3. 0.003  100 4. 0.003  100 5. 104 6. 10–4 7. 230 123,000 0.123 0.3 0.00003 10,000 0.0001 1

  2. Scientific Notation

  3. Do you know your place? 123456.54321 Label the place value of each digit The first one is done for you!

  4. 123456.54321 1 10000 100 100000 1000 10

  5. So what does this mean? • If the exponent is positive, the base is used as a factor! • Example 43 = 4∙4 ∙4 = 64 • If the exponent is negative, the base is used as a divisor! • Example :

  6. Nanotechnology - nano- is a prefix that is attached to a word to describe its size. • Write this number on your paper. 3,000,000,000,000,000,000,000,000,000,000,000,000,000,000 • Double-check your answers. Are your numbers correct? What difficulties did you run into while transferring this number to your papers? If you were doing an experiment and this number was part of your data, would it pose a problem?

  7. Scientific Notation • Scientific Notation is a way of writing extremely large and extremely small numbers without all of the zeros. • a number expressed in scientific notation contains two parts: • A number ≥ 1 but < 10 ; • A power of 10 that multiplies that number. This power of 10 represents the new location of the shifted decimal point.

  8. Converting Large Numbers • to convert a large number to scientific notation. Ex: 3,000,000,000,000,000,000,000,000,000,000,000,000,000,000 • Move the decimal place to the left until the numeric value is between 1 and 10. This number is A in the equation in step 3. • Count the number of places the decimal point was moved. This is B is step 3. • Rewrite the number in the following equation: A x 10B The scientific notation for the number on the board is: 3 x 1042.

  9. Converting Very Small Numbers • to convert very small numbers into scientific notation. Ex: 0.00000000025. • Move the decimal place to the right until the numeric value is between 1 and 10. This number is A in the equation in step 3. • Count the number of places the decimal point was moved. This is B is step 3. Note: B is always negative with small numbers. • Rewrite the number in the following equation: A x 10-B The scientific notation for the number is: 2.5 x 10-10.

  10. Multiplying by Powers of 10 You can also move the decimal point to find the value of any number multiplied by a power of 10. You start with the number rather than starting with 1.

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