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Scientific Notation and Significant Figures

Scientific Notation and Significant Figures. A positive exponent means move the decimal to the right Ex. 1.34 x 10 4 = 13,400 A negative exponent means move the decimal to the left Ex. 5.12 x 10 -2 = 0.0512 Now try some!!. Going from scientific notation to standard number form.

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Scientific Notation and Significant Figures

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  1. Scientific Notation and Significant Figures

  2. A positive exponent means move the decimal to the right • Ex. 1.34 x 104 = 13,400 • A negative exponent means move the decimal to the left • Ex. 5.12 x 10-2 = 0.0512 Now try some!! Going from scientific notation to standard number form.

  3. Numbers in scientific notation should begin with a number between 1 and 10 and then should be followed by “x 10” with an exponent. • Large numbers will have a positive exponent • Ex. 67,000 = 6.7 x 104 • Small numbers will have a negative exponent • Ex. 0.000031 = 3.1 x 10-5 Now try some!!! Going from standard number form to scientific notation

  4. Adding/Subtracting Rules • Numbers must have the SAME exponent • Then, just add the numbers as normal and keep the original exponent • Ex. 3.3 x 103 + 2.1 x 103 = 5.4 x 103 Now try some!!! Math with scientific notation!

  5. What if they are not the same?? • If exponents are not the same, one must be adjusted • Example: 7.1 x 104 – 2.0 x 103 • 7.1 x 104 can become 71 x 103 • 2.0 x 103 can become .2 x 104 Now try some!!! Exceptions

  6. Multiplying • When multiplying numbers in scientific notation, the exponents are added • Ex. 3.0 x 103 * 2.0 x 104 = 6.0 x 107 • Dividing • When dividing numbers in scientific notation, the exponents are subtracted • Ex. 9.0 x 105 / 3.0 x 102 = 3.0 x 103 • Ex. 3.0 x 103 / 2.0 x 104 = 1.5 x 10-1 Multiplying and Dividing

  7. When rounding, we make certain numbers “insignificant” therefore there are rules with respect to which numbers matter in chemistry • These are called “sig figs” Significant Figures

  8. All non-zeros ARE significant • Examples: 1.23 has three sig figs 41.12 has four sig figs • Zeros between non-zeros ARE significant • Examples: 1205 has four sig figs 1.3021 has five sig figs The Rules

  9. Placeholder zeros are NOT significant • Examples: 34,000 has two sig figs 0.0002 has one sig fig but…. 34,001 has five sig figs… why? • Final zeros after a decimal ARE significant • Examples: 1.200 has four sig figs 34,000.00 has seven sig figs The Rules

  10. How many sig figs do the following have? • 3.002 • 12,000 • 12,000.00 • 0.009 • 12 Now try some!!! Practice!!

  11. Adding/Subtracting • Answer should have the same number of DECIMAL PLACES as the original number with the LEAST amount of decimal places • Example: 1.12 + 2.3 = 3.42 Math with Sig Figs

  12. Multiplying/Dividing • Answer should have the same number of SIG FIGS as the original number with the LEAST amount of sig figs. • Examples: • 3.40 x 1.2 = 4.08  4.1 • 7 x 24 = 168  200 • 14.000 x 2.00 = 28 = 28.0 • 45,000 x 112 = 5,040,000  5.0 x 106 Math with Sig figs

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