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Scientific Notation

Scientific Notation. Chemistry. Scientific Notation. Expresses numbers as a multiple of two factors: A number between 1- 10 10 raised to a power or exponent 6.23 x 10 23 . Scientific Notation. When numbers larger than 1 are expressed in scientific notation, the exponent is positive.

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Scientific Notation

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  1. Scientific Notation Chemistry

  2. Scientific Notation • Expresses numbers as a multiple of two factors: • A number between 1- 10 • 10 raised to a power or exponent 6.23 x 10 23

  3. Scientific Notation • When numbers larger than 1 are expressed in scientific notation, the exponent is positive. 2.0 x 10 3= 2000 • When numbers smaller than 1 are expressed in scientific notation, the exponent is negative. 2.0 x 10 -3 = 0.002

  4. Scientific Notation • Moving the decimal. • The exponent just tells you how many times you had to move the decimal. • Positive exponent, we move to the left. + - • Negative exponent, we move to the right.

  5. Practice • Express the following in scientific notation: • 700m • 38 000m • 4 500 000m • 685 000 000 000m

  6. Answers • 7 x 10 2 • 3.8 x 10 4 • 4.5 x 10 6 • 6.85 x 10 11

  7. Practice • Express the following in scientific notation: • 0.0054 kg • 0.000 006 kg • 0.000 000 076 kg • 0.000 000 000 8 kg

  8. Answers • 5.4 x10 -3 • 6 x 10 -6 • 7.6 x 10 -8 • 8 x 10 -10

  9. Adding and Subtracting Scientific Notation Chemistry A

  10. Adding & Subtracting • When we add or subtract with these numbers the first thing we must do is make sure the exponents are the same for both number. 7.35x 10 2 + 2.43x102 We just add 7.35 and 2.43, don’t worry about adding the exponents. =9.78x102

  11. Adding & Subtracting • Must make exponents the same before you continue to add or subtract. 5.40 x 10 3 + 6.00 x 10 2 We must move the decimal to make them the same. • The decimals must be aligned 5.40 x 10 3 + 0.60 x 10 3 6.00 x 10 3

  12. If the exponents are not the same then we must make them match each other. • We will match it to the first number if and only if the first number is between 1-10. 2.50 x 10 4 + 6.50 x10 3 6.50 x 10 3=.650 x10 4 2.50 x 10 4 + .650 x10 4 3.15 x 10 4

  13. Practice • 5 x 10 -5 + 2 x10 -5 7 x 10 -5 • 4 x 10 -12 + 1 x10 -12 5 x10 -12 • 1.26 x 10 4 + 2.5 x10 3 1.51 x 10 4 • 7.06 x 10 -3 + 1.2 x10 -4 7.18 x 10 -3

  14. Subtracting • Is basically the same thing, except we’re subtracting instead of adding. • We still have to make sure that the exponents are the same.

  15. 9 x 10 2 - 7 x10 2 2 x 10 2 • 7 x 10 8 - 4 x10 8 3 x10 8 • 4.39 x 10 5 – 2.8 x10 4 4.11 x 10 5 • 5.36 x 10 -1 – 7.40 x10 -2 4.62 x 10 -1

  16. Multiplying & Dividing • We multiply or divide the coefficients (decimal numbers) and add or subtract the exponents. • 3.0 x 10 4 x 2.0 x 10 2 = • (3.0 x 2.0) x 10 (4+2) = • 6.0 x 10 6

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