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Bell? /DLO

Bell? /DLO. DLO. Bell ?. Be able to count and use significant figures Be able to measure properly. What are sig figs…again?. Significant Figures. Identifying and Working with Significant figures. Significant Figures. There is a limit to the number of digits a measurement can have.

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Bell? /DLO

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  1. Bell? /DLO DLO Bell ? Be able to count and use significant figures Be able to measure properly What are sig figs…again?

  2. Significant Figures Identifying and Working with Significant figures

  3. Significant Figures There is a limit to the number of digits a measurement can have. This limit communicates the significance of the numbers in the measurement. For example, 35 meters is not as significant or precise a measurement as 35.319 meters. In the first measurement there is less certainty in the measurement since it is only accurate to the tens place, while the second is accurate to the thousandths place.

  4. What is a significant figure? • Significant figures are the following: • Any non-zero number • Zeroes in some cases but not others • I’m sure that was really clear so lets look at a few examples.

  5. Tricks for determining significant figures • Here are some tricks to help you figure out how many significant figures are in a number. • Look at the number and see if a decimal is present or absent. • 365- • 3.03- • 300- • 0.003- • 3050- • 3.00- • 3.0120-

  6. Tricks for determining significant figures 3.03 Atlantic Pacific • If the decimal is PRESENT start from the PACIFIC side of the number and find the first non-zero number. • That first non-zero number that you come to and everything to the right of that number are significant digits. • 365- • 3.03- • 300- • 0.003- • 3050- • 3.00- • 3.0120-

  7. Tricks for determining significant figures 365 Atlantic Pacific • If the decimal is ABSENT start from the ATLANTIC side of the number and find the first non-zero number. • That first non-zero number that you come to and everything to the left of that number are significant digits. • 365- • 3.03- • 300- • 0.003- • 3050- • 3.00- • 3.0120-

  8. Significant Figures in Math In most cases you will be working with the same measurement tool which means you will have the same number of significant figures. Sometimes you will have numbers from two different tools which could mean two different sets of significant figures. In the last case you will need to make adjustments in your final answer to account for the significant figures in your problems.

  9. Significant Figures-Addition & Subtraction When adding and subtracting numbers, the answer cannot have more significant places past the decimal than the least accurate number. Example:

  10. Significant Figures-Multiplication & Division When multiplying and dividing numbers the answer cannot have more significant digits than the number with the least significant digits. Example:

  11. Count the number of significant figures: 1) 1600 2) 11.0 3) 253 4) .0000890 5) 0.0103 Trailing zeroes count when there is a decimal point present All Nonzero numbers count All Nonzero numbers count Trailing zeroes count when there is a decimal point present All Zeroes before nonzero numbers NEVER Count! In between Zeroes ALWAYS count

  12. Qz Cont’d Write the Answer to the following problems USING CORRECT SIGNIFICANT FIGURES 6) 5.45 + 11.0   7) 14.5678 - 12.001   8) 2.68 ÷ .04   9) (113.2 x 5) + 11.45   10) 1.92 x 103 rounded=16.5 Decimal Unrounded=16.45 2 #’s after 1 #’s after Decimal U.R=2.5668 rounded=2.567 4 #’s after 3 #’s after Sig Figs U.R=67 rounded=70 3 SF 1 SF Sig Figs U.R=577.45 rounded=600 1 SF 4 SF 3 SF Sig Figs Answer=1920 3 SF

  13. Scientific Notation

  14. Scientific Notation In science the numbers can be extremely large or small and becomes inconvenient to write numbers with a lot of zeroes. For example the value for something is 0.000000000382 which is not only a pain to write but also difficult to say. We use scientific notation to clean it up. Doing so makes this number 3.82 x 10-10 How did I do that?

  15. Scientific Notation • First start with the number and moving the decimal • If the number is small move the decimal behind the first non-zero number 0.000372 → 3.72 • Now you have to account for the zeroes you replaced by using a power of 10. • Count how many places you moved the decimal. This is the exponent for the power of 10. • If you moved the decimal to the left the exponent is positive, to the right is negative. 3.72 x 10 -4

  16. Scientific Notation • First start with the number and moving the decimal • If the number is large move the decimal behind the last non-zero number 37200 → 3.72 • Now you have to account for the zeroes you replaced by using a power of 10. • Count how many places you moved the decimal. This is the exponent for the power of 10. • If you moved the decimal to the left the exponent is positive, to the right is negative. 3.72 x 10 4

  17. Using Scientific Notation Not only does it make it easier to express numbers but it also can help you express them with the correct significant figures. Suppose you are asked to express 200, 000 with only 3 significant figures. See if you can figure it out using scientific notation. Keep in mind that the final number must be written so that it is greater than 1 and less than 10.

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