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Scientific Notation

Section 1.2. Scientific Notation. Why use it?. Some numbers are too big or too small to write using regular form (also called standard notation) Using Scientific Notation often makes it easier to multiply or divide numbers without a calculator

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Scientific Notation

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  1. Section 1.2 Scientific Notation

  2. Why use it? • Some numbers are too big or too small to write using regular form (also called standard notation) • Using Scientific Notation often makes it easier to multiply or divide numbers without a calculator • How would you express an answer of 50000 L to only 3 significant digits?

  3. What does it look like? • Scientific Notation takes the form Coefficient × 10exponent Coefficient is always ≥ 1 but < 10. The exponent is either a positive or negative whole number.

  4. What does the exponent tell me? • Exponents less than 0 • These are numbers that are smaller than 1 • Exponents equal to 0 • The number is between 1 and 10. • Exponents greater than 0 • The number is greater than 10.

  5. Here’s how to use it: • Take any number, let’s say… 503 • To turn it into scientific notation, place a decimal point that results in a number between 1 and 10. • You moved it 2 places to the left. Remember that number. 5.03

  6. And now for the exponent… 5.03 is what you got from the previous step. You moved the decimal point 2 places to the left to get there, so use 2 for your exponent. 5.03 × 102

  7. One more example • Turn this number into scientific notation: 0.0000341 • To turn it into scientific notation, move the decimal place until you get the coefficient! • You moved it 5 places to the right. Remember that number. 0.00003.41

  8. And now for the exponent… 3.41 is what you got from the previous step. You moved the decimal place 5 places to the right to get there, so use -5 for your exponent. 3.41 × 10-5

  9. Multiplying Scientific Notation • When multiplying two scientific notation numbers together… • MULTIPLY the coefficients • ADD the exponents

  10. Example: Multiply: (3.2 × 103) × (4.0 × 105) • MULTIPLY the coefficients 3.2 × 4.0 = 12.8 • ADD the exponents 3 + 5 = 8 • The result is… 12.8 × 108 • Converting to accepted scientific notation… 1.28 × 109

  11. Dividing Scientific Notation • When dividing two scientific notation numbers… • DIVIDE the coefficients • SUBTRACT the exponents

  12. Example: Divide: (6.4 × 103) ÷ (2.0 × 105) • DIVIDE the coefficients 6.4 ÷ 2.0 = 3.2 • SUBTRACT the exponents 3 - 5 = -2 • The result is… 3.2 × 10-2

  13. Scientific Notation and significant digits • 6.23 x 102 K has how many sigfigs? • 1.00023 x 10-2 m? • How would you express an answer of 50000 L to 3 significant digits? • 5.00 x 104 L (this cannot be done using standard notation)

  14. Useful exponents to memorize • 10-9nano- (billionth) • 10-6 micro- (millionth) • 10-3milli- (thousandth) • 10-2centi- (hundredth) • Base • 103 kilo- (thousands) • 106 mega- (millions) • 109giga- (billions)

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