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SIGNIFICANT FIGURE RULES

SIGNIFICANT FIGURE RULES. REASON: ERROR CAN MULTIPLY AND ACCUMMULATE WHEN WE DO MATHEMATICAL OPERATIONS. WE MUST HAVE A WAY TO DEAL WITH ERROR IN OUR MEASUREMENTS. NONZEROS. THE RULE: ALL NONZEROS ARE SIGNIFICANT ! DEFINITION: ANY DIGIT THAT IS NOT ZERO

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SIGNIFICANT FIGURE RULES

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  1. SIGNIFICANT FIGURE RULES • REASON: ERROR CAN MULTIPLY AND ACCUMMULATE WHEN WE DO MATHEMATICAL OPERATIONS. • WE MUST HAVE A WAY TO DEAL WITH ERROR IN OUR MEASUREMENTS.

  2. NONZEROS • THE RULE: ALL NONZEROS ARE SIGNIFICANT ! • DEFINITION: ANY DIGIT THAT IS NOT ZERO • ALL NONZEROS ARE IMPORTANT IN THE EXPRESSION • EXAMPLES ARE 1,2,3,4,5, … . • THE EXPRESSION 3653 HAS FOUR SIGNFICANT FIGURES.

  3. CAPTIVE ZEROS • THE RULE: ALL CAPTIVE ZEROS ARE SIGNIFICANT! • DEFINITION: ZEROS THAT FALL BETWEEN NON ZERO DIGITS • THESE ZEROS ARE ALSO IMPORTANT! • EXAMPLES: 203 HAS 3 SF’S, 40005 HAS 5 SF’S, 6006309 HAS 7 SF’S

  4. TRAILING ZEROS • THE RULE: ALL TRAILING ZEROS ARE SIGNIFICANT! • DEFINITION: ZEROS THAT FALL AT THE END OF A NUMBER AND TO THE RIGHT OF AN EXPLICIT DECIMAL PLACE! • THEY ARE IMPORTANT! • EXAMPLES: 3.900 HAS 4 SF’S, 1.0500 HAS 5 SF’S

  5. LEADING ZEROS • THE RULE: ALL LEADING ZEROS ARE NOT SIGNFICANT ! • DEFINITION: ZEROS AT THE BEGINNNG OF A NUMBER • THESE ARE FOR THE PURPOSE OF PLACING DECIMALS ONLY! • THEY ARE NOT IMPORTANT IN DETERMINING THE ACCURACY AND PRECISION OF THE NUMBER! • EXAMPLES: 0.0036 HAS 2 SF’S, 0.00030 HAS 2 SF’S, 0.030300 HAS 5 SF’S

  6. FUZZY ZEROS • THE RULE: MAY OR MAY NOT BE IMPORTANT! • DEFINITION: ZEROS AT THE END OF A NUMBER WHERE THERE IS AN IMPLICIT (OR IMPLIED) DECIMAL • IF ENCOUNTERED, FUZZY ZEROS ARE CONSIDERED NOT SIGNIFICANT ! • CLEARING UP THE “FUZZINESS” IS DONE BY PUTTING NUMBERS IN SCIENTIFIC NOTATION! DON’T LEAVE NUMBERS FUZZY! • USE SCIENTIFIC NOTATION TO ELIMINATE CONFUSION. • THEY MUST BE CONSIDERED NOT SIGNIFICANT IF LEFT FUZZY! • EXAMPLE: 34000 HAS ONLY 2 SF’S

  7. EXACT NUMBERS • COUNTING NUMBERS • EXACT NUMBERS AND COUNTING NUMBERS ARE INFINITELY SIGNIFICANT! • EXACT CONVERSION FACTORS • HAVE INFINITE SIGNIFICANCE • 12 EGGS = 1 DOZ. • 12 EGGS = 12.00000000000000….. • 760mmHg = 1 atm • 760.000000… = 1.000000…

  8. SIGNIFICANT FIGURES • ALL NONZEROS ARE SIGNIFICANT ! • ALL CAPTIVE ZEROS ARE SIGNIFICANT! • ALL TRAILING ZEROS ARE SIGNIFICANT ! • ALL LEADING ZEROS ARE NOT SIGNFICANT ! • ALL FUZZY ZEROS ARE CONSIDERED NOT SIGNIFICANT ! (USE SCIENTIFIC NOTATION TO ELIMINATE CONFUSION) • EXACT NUMBERS AND COUNTING NUMBERS ARE INFINITELY SIGNIFICANT!

  9. ADDITION / SUBTRACTION RULE • YOU CAN ONLY HAVE AS MANY DECIMAL PLACES AS THE NUMBER WITH THE LEAST DECIMAL PLACES. • “LEAST ACCURACY DETERMINES FINAL ACCURACY”

  10. MULTIPLICATION / DIVISION RULE • YOU CAN ONLY HAVE AS MANY SIGNIFICANT DIGITS AS THE NUMBER WITH THE LEAST NUMBER OF SIGNIFICANT DIGITS. • “LEAST SIGNIFICANCE DETERMINES FINAL SIGNIFICANCE”

  11. SIGNIFICANT FIGURES • ALL NONZEROS ARE SIGNIFICANT ! • ALL CAPTIVE ZEROS ARE SIGNIFICANT! • ALL TRAILING ZEROS ARE SIGNIFICANT ! • ALL LEADING ZEROS ARE NOT SIGNFICANT ! • ALL FUZZY ZEROS ARE CONSIDERED NOT SIGNIFICANT ! (USE SCIENTIFIC NOTATION TO ELIMINATE CONFUSION) • EXACT NUMBERS AND COUNTING NUMBERS ARE INFINITELY SIGNIFICANT! • ADDITION / SUBTRACTION RULE: YOU CAN ONLY HAVE AS MANY DECIMAL PLACES AS THE NUMBER WITH THE LEAST DECIMAL PLACES. • MULTIPLICATION / DIVISION RULE: YOU CAN ONLY HAVE AS MANY SIGNIFICANT DIGITS AS THE NUMBER WITH THE LEAST NUMBER OF SIGNIFICANT DIGITS.

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