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# Significant digits

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### Significant digits

1. 1. Everything you wanted to know about Significant Digits… … but were afraid to ask
2. 2. What is a good way to express calculated numbers?  Are these?  2 x 3.00 = 6.00  14.00000 ÷ 2.1 = 6.66666  How about these?  2 x 3.00 = 6  14.00000 ÷ 2.1 = 6.7
3. 3. Calculated answers need to have a balance between accuracy and precision to account for the QUALITY of measure  Accuracy: In science, engineering, industry and statistics, accuracy is the degree of conformity of a measured or calculated quantity to its actual, nominal, absolute, or some other reference, value…It’s “correctness”  Precision: The precision of a measurement or value describes the number of digits that are used to express that value. This might be the total number of digits (sometimes called the significant digits)…How well was it measured
4. 4. SOME clarification  Significant Figure (sig-fig): How well a measurement was taken  Significant Digit (sig-dig): How well we can express a calculated answer to account for sig-figs  Scientific notation: A base 10 method of expressing large answers
5. 5. Significant Figure  A way to express the quality of a measured value Rule of thumb: Estimate one and only one number beyond what you can read from the instrument
6. 6. Significant digit  A way to express the quality of measured value in a calculated answer using a balance of precision and accuracy
7. 7. Scientific Notation 1) One and only one integer left of the decimal 2) When converting from a number larger than one-move decimal left and express exponent positively 3) When converting from a number less than one-move decimal right and express exponent negatively
8. 8. Rules for determining how many significant digits exist in a number 1) All Integers count 2) Zeros contained between integers count 3) All trailing zeros count as along as a decimal point is expressed in the number. If there is no decimal, then the trailing zeros are only significant if it is a measurement. 4) Preceding zeros do not count as they are simply placeholders
9. 9. Rules for determining which value dictates the expressed number  Multiplication and division: The number with the least sig-figs determine how many numbers you will use to express your answer Example: 4.44 ÷ 4 = 1.11 but expressed as 1  Addition and subtraction: The number with the least number of decimal places determines which number of sig figs, you will use to express your answer in. If there is a tie, refer to multiplication/division rule. Example: 3.11-1.3-.055-1= .755 but expressed as 8 X 10-1
10. 10. Rules for rounding values  All rounding rules apply as usual UNLESS the number ends in 5  When you have an answer which ends with a 5 and you need to express it with one less integer, use these rules:  1) If the number preceding the 5 is odd then round up  2) If the number preceding the 5 is even then leave it alone.  1.0975 is expressed as 1.098.  1.0985 expressed 1.098  THIS ONLY APPLIES IF THE NUMBER ENDS IN 5 AND YOU HAVE TO EXPRESS IN ONE NUMBER LESS
11. 11. Practice Time  How many sig-figs are in the following measured values?  2.555  .0000056  1.000055  45.9000000000
12. 12. Answers  2.555-4  .0000056-2  1.000055-7  45.9000000000-12
13. 13. Expression practice problem  Based on the rules, what is the proper expression of the answer in the problem below?  3.00 X 6 =
14. 14. Answer  The sig-digs are determined by the least number of sig-figs when multiplying or dividing  3.00 X 6 = 18.000 but expressed in sig-digs as 2 X 101 because you can’t express 18 as 1 sig-dig
15. 15. One More  Use the sig-figs in the problem below to determine how many sig-digs to express the answer.  1.00 + 2.111 + 2,254 =
16. 16. Answer The sig-fig with the least decimal places determines the number of sig-digs to express the answer  1.00 + 2.111 + 2,254 = 2257.111 but expressed as 2,257 or 2.257 x 103 because 2254 has the least decimal places and has sig-fig equal to 4
17. 17. Disclaimer  Sig-digs are NOT the most important concept in chemistry…they do help you express yourself more intelligently and thus can add to your popularity
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