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Significant Digits

Significant Digits. ….or “Sig Digs”, if you prefer. Sometimes called “Significant figures”. That’s right: “Sig Figs”. Anyway…. First, some rules:. 1. All non-zero digits ARE significant. 1, 2, 3, 4, 5, 6, 7, 8, 9. Example: the number “5691” has… _____ sig digs. 4.

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Significant Digits

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  1. Significant Digits ….or “Sig Digs”, if you prefer. Sometimes called “Significant figures” That’s right: “Sig Figs” Anyway…..

  2. First, some rules: 1. All non-zero digits ARE significant. 1, 2, 3, 4, 5, 6, 7, 8, 9. Example: the number “5691” has… _____ sig digs. 4

  3. Next Rule: • Zeros between other sig digs • ARE significant. Example: the number “204017” has ____ sig digs. 6

  4. 3rd Rule: (hold on tight- this is where it gets a little complicated…) 3. Zeros to the right of the decimal place and …to the right other sig digs ARE significant. Example: The number “1.000” has ____ sig digs. 4

  5. Last Rule: 4. All other zeros are NOT significant. …they are just “place holders”. Confused? Lets do some examples….

  6. Examples: 2 .00081 has ____ sig dig(s). (only) 1 100 has ____ sig dig(s). 4 100.0 has ___ sig dig(s). 3 54900 has ____ sig dig(s).

  7. Multiplying & Dividing: So what’s the big deal? “A chain is only a strong as it’s….. Remember the old saying: …weakest link”? Same kind of idea with sig digs:

  8. Multiplying & Dividing: A calculated number is only as accurate as …. …the least accurate measured number that went into that calculation. In other words: Your answer should have no more (and no less) sig digs than the least number that went into that calculation. OK- more examples….

  9. Multiplying & Dividing: 12.6 divided by 5.1 Your calculator would say…. 2.470588235 But you should only report the answer as… 2.5 (5.1 has only 2 sig digs) Round up when appropriate.

  10. Multiplying & Dividing: One more example: • 6.000 x 63451222 Your calculator would say… 380707332 But you should only report 380700000 since 6.000 has only 4 sig digs.

  11. Multiplying & Dividing: OK- last one, really…. …how ‘bout: 2.00 x 1.500 The answer is just “3”, right…? Nope- you need to report your answer as 3.00 (remember- answers can have no more but no less sig digs than the least number that went into the calculation.)

  12. Adding & Subtracting This rule is a little different. This time, it’s limited to the least sensitive decimal place. So, with adding & subtracting, you don’t need to count sig digs, You look at decimal places!!!

  13. Example: 3.9 + 12.479 + 3.49 When added gives you 19.869 HOWEVER: Since 3.9 in the above problem only goes to the tenths place…. You must only report your answer to the tenths place: 19.9 Notice: you can have as many sig digs as you need, as long as you keep to the least sensitive decimal place.

  14. So to review: For multiplying & dividing: Count sig digs in the equation and limit the answer to the least number. For adding & subtracting: Look for the least number of decimal places and limit it that way.

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