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Scientific (Exponential) Notation

Scientific (Exponential) Notation. Large and small numbers- common in science!. There are 602 200 000 000 000 000 000 000 items in 1 mole of anything. Or you could say there are 602 200 000 000 000 000 000 000 atoms of hydrogen in 1.011 grams of hydrogen

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Scientific (Exponential) Notation

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  1. Scientific (Exponential) Notation

  2. Large and small numbers- common in science! • There are 602 200 000 000 000 000 000 000 items in 1 mole of anything. • Or you could say there are 602 200 000 000 000 000 000 000 atoms of hydrogen in 1.011 grams of hydrogen • 405 696 000 meters from Earth to the Moon • There are 602 200 000 000 000 000 000 000 molecules of water in 18.02 grams of water. • We’ll use this number A LOT!

  3. Scientific Notation • Definition: Number written as a product of 2 numbers- the coefficient and 10 raised to a power • The number must be written with one number to the left of the decimal and the rest to the right of the decimal • The exponent indicates how many places the decimal should be moved right or left • If a number is less than 1, the exponent will be negative • If a number is greater than 1, the exponent will be positive

  4. Scientific Notation- Positive Exponents • 4 000 000 000 • Move the decimal 9 places to the left. • Re-write as 4 x 109 • 15.9 x 105 • There can only be one number to the left of the decimal, so move the decimal 1 place to the left • Re-write as 1.59 x 106 • Both numbers mean 1 590 000

  5. Scientific Notation- Positive Exponents • Re-write this number in normal notation: 4 x 109 • The 9 means that the decimal must be moved 9 times. • The positive indicates that the final number will be larger than 1. • 4 000 000 000

  6. Scientific Notation- Negative Exponents • 0.000 000 0578 • Move the decimal 8 times to the right to get just one number left of the decimal • When the number is smaller than one, the exponent is negative, so re-write the number as 5.78 x 10-8 • 458.8 x 10-7 • Not in scientific notation- too many #s left of the decimal • Move the decimal two places to the left, which is the opposite way the decimal was moved to get the -7. • This makes the -7 into a -5 • Re-write as 4.588 x 10-5 • Think of it as “undoing” 2 places indicated by the exponent • Both numbers still mean: 0.000 045 88

  7. Math and Scientific Notation • Adding and Subtracting • Move the decimal and change the exponent accordingly until both numbers have the same exponent • Add or Subtract the coefficients • Write the exponent at the end • Convert to Scientific Notation

  8. Addition and Subtraction • Example: • 4.3 x 105 + 6.7 x 107 • Change both to the same exponent: • 4.3 x 105 + 670 x 105 = 674.3 x 105

  9. Math and Scientific Notation • Multiplication • multiply the coefficients as usual • ADD the exponents • Move the decimal and change the exponent until the number returns to scientific notation • Example: • (4.3 x 105 )(6.7 x 107 ) = 28.81 x 1012

  10. Math and Scientific Notation • Division: • Divide the coefficients as usual • SUBTRACT the exponents • Move the decimal and change the exponent until the number returns to scientific notation • Example: • 8.8 x 106 / 2 x 102 = 4.4 x 104

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