# NOTES – SIGNIFICANT FIGURES (SIG FIGS) ANY DIGIT OF MEASUREMENT KNOWN WITH CERTAINTY PLUS ONE FINAL DIGIT WHICH IS ESTIMATED.

## Presentation on theme: "NOTES – SIGNIFICANT FIGURES (SIG FIGS) ANY DIGIT OF MEASUREMENT KNOWN WITH CERTAINTY PLUS ONE FINAL DIGIT WHICH IS ESTIMATED."— Presentation transcript:

NOTES – SIGNIFICANT FIGURES (SIG FIGS) ANY DIGIT OF MEASUREMENT KNOWN WITH CERTAINTY PLUS ONE FINAL DIGIT WHICH IS ESTIMATED.

ACCURACY AND PRECISION SIG FIGS HAVE TO DO MORE WITH THE ACCURACY OF A MEASUREMENT THAN PRECISION. ACCURACY – HOW CLOSE A MEASUREMENT IS TO ITS ACCEPTED VALUE. PRECISION – HOW CLOSE A SET OF MEASUREMENTS ARE TO EACH OTHER.

ACCURACY & PRECISION SUPPOSE A SET OF MEASUREMENTS OF A SAMPLE OF GOLD ARE AS FOLLOWS: 1. 25 g, 1.28 g, 1.30 g, 1.24 g THE ACCEPTED MASS OF THE SAMPLE IS 2.20 GRAMS. ARE THE MEASUREMENTS PRECISE? ARE THE MEASUREMENTS ACCURATE?

ACCURACY AND PRECISION WHICH PICTURE IS PRECISE, ACCURATE, BOTH, NEITHER? KNOW THE DIFFERENCE AND BE ABLE TO EXPLAIN WHY THE PICTURE ABOVE IS __________ __________ THE PICTURE ABOVE IS __________ __________

ACCURACY AND PRECISION IS IT POSSIBLE TO HAVE PRECISION WITHOUT ACCURACY? WHY/WHY NOT? IS IT POSSIBLE TO HAVE ACCURACY WITHOUT PRECISION? WHY/WHY NOT?

SIG FIGS AND ACCURACY REMEMBER THE RULE OF DETERMINING THE NUMBER OF SIG FIGS. FOR ANY MEASUREMENT. YOU CAN ALWAYS ESTIMATE ONE DECIMAL PLACE SMALLER THAN THE SMALLEST GRADUATION ON THE MEASURING INSTRUMENT.

EXAMPLE OF ESTIMATIONS WHAT IS THE BEST ESTIMATE OF THIS MEASUREMENT (REMEMBER YOUR RULE) IF YOU ANSWERED AROUND 0.6 M, THAT IS RIGHT! (INCREMENT IS ONES PLACE)

EXAMPLE OF ESTIMATIONS WHAT IS THE BEST ESTIMATE OF THIS MEASUREMENT? IF YOUANSWERED 66 CM, YOU ARE RIGHT

EXAMPLE OF ESTIMATIONS WHAT IS THE BEST ESTIMATE OF THIS MEASUREMENT? APPROXIMATELY 64.5 CM

RULES TO DETERMINE THE NUMBER OF SIG FIGS. 1. ALL NONZERO DIGITS ARE SIGNIFICANT (MEANING THEY CAN DEFINITELY BE MEASURED). 2. ZEROS BETWEEN NON-ZERO DIGITS ARE ALWAYS SIGNIFICANT.

RULES TO DERMINE THE NUMBER OF SIG FIGS. 3. ZEROS IN A MEASUREMENT WHERE THERE IS NO DECIMAL POINT ARE NOT SIGNIFICANT, EXCEPT AS IN RULE #2. HOW MANY SIG FIGS ARE IN THESE MEASUREMENTS?  A. 2500 cmB. 1001 m  C. 125 gD. 48080900 L

ZERO AS A SIG FIG. 4. ZEROS ARE SIGNIFICANT IF A DECIMAL POINT IS PRESENT AND THEY ARE PRECEDED BY A NON-ZERO DIGIT. HOW MANY SIG FIGS ARE IN THESE MEASUREMENTS?  A. 2500. CMB. 2500.0 CM  C. 0.025 CMD. 0.0006700300 CM

MORE PRACTICE COUNTING SIG FIGS. 1. 5.345 x 10 -3 L 2. 0.00073 m 3. 4.200 x 10 5 dL 4. 40.007 G 5. 50, 700 mm6. 0.070020 km 8. 1,000,000 miles 8. 0.000003 L 9. 100 inches 10. 70. mm 11. 70.0 mm 12. 70 mm 13. 300 cars

ROUNDING OFF TO A CERTAIN NUMBER OF SIG FIGS. SOMETIMES WE HAVE TO ROUND MEASURMENTS OFF TO A CERTAIN NUMBER OF SIG FIGS. EXAMPLES:  ROUND 107.5 m TO 2 SIG FIGS.  ROUND 7.30 CM TO 1 SIG FIG  ROUND 4.7530 x 10 -3 TO 2 SIG FIGS  ROUND 0.0003440 km TO 1 SIG FIG.

HANDLING MEASUREMENTS USING SIG FIGS. ANOTHER RULE - WHENEVER WE USE MEASUREMENTS IN A MATHEMATICAL CALCULATION, WE CAN NOT BE MORE ACCURATE THAN OUR LEAST ACCURATE MEASUREMENT. THEREFORE, WE CAN NOT USE MORE SIG FIGS THAN OUR MEASUREMENT WITH THE LEAST NUMBER OF SIG FIGS.

MULTIPLYING AND DIVIDING WITH SIG. FIGS. THE NUMBER OF SIG FIGS IN YOUR ANSWER CAN NOT BE MORE THAN THE FEWEST GIVEN SIG FIGS. EXAMPLES:  0.250 CM x 2.0 CM =  5.0 M x 5.0 M =  5 M x 5.0 M =  5 M x 5 M =  640.0 M 2 / 8 M =

ADDING AND SUBTRACTING WITH SIG FIGS. DON’T USE SIG FIGS, LOOK AFTER DECIMAL POINT RULE – OUR ANSWER CANNOT CONTAIN MORE DIGITS AFTER THE DECIMAL POINT THAN THE LEAST NUMBER OF DIGITS AFTER THE DECIMAL POINT GIVEN (ZEROS COUNT HERE!) ROUND AFTER THE OPERATION EXAMPLES:  1. 6.000 M + 0.06 M =  2. 0.8 CG - 0.243 CG =

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