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 ALL NONZEROS ARE IMPORTANT IN THE EXPRESSION EXAMPLES ARE 1,2,3,4,5, …. THE EXPRESSION 3653 HAS FOUR SIGNFICANT FIGURES.

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, HAS 5 SF’S, HAS 7 SF’S

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: HAS 4 SF’S, HAS 5 SF’S

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: HAS 2 SF’S, HAS 2 SF’S, HAS 5 SF’S

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: HAS ONLY 2 SF’S

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

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. “LEAST ACCURACY DETERMINES FINAL ACCURACY”

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”

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.