SIGNIFICANT FIGURES
DEFINING SIGNIFICANT FIGURES Any measurement made is only as detailed and accurate as the tool used to make the measurement.
ESTIMATE 1 DIGIT As a scientists uses a tool, the scientist reads the markings on the tool, and then estimates one more place. volume = 6.60 ml This tool s markings measure to the nearest whole number. This tool s markings also measure to the tenths place. The accuracy of the ones place and tenths place are guaranteed. The number in the hundredths place is estimated. The rule is only one digit/number in a measurement is estimated. This rule ensures accuracy in data collection.
The orange bar is 14.61 cm in length. THIS TOOL MEASURES ACCURATELY THE TENS PLACE ONES PLACE TENTHS PLACE A SCIENTISTS WOULD ESTIMATE THE HUNDREDTHS PLACE
RULES FOR SIGNIFICANT FIGURES While reading someone else s measurement, you need to evaluate which digits were accurately measured, and which digits were estimated. We call the accurate measurements significant figures (sig figs) or significant digits. 1. All non zero digits are significant. 5. ALL DIGITS in an equivalency OR Ex. 456 ml 3 sig figs counting numbers are significant Ex. 22 ml 2 sig figs 2. Sandwich zeros are significant. Ex. 100 cm = 1 m or 12 in = 1 foot Ex. 406 g 3 sig figs All are significant Ex. 3005 g 4 sig figs 3. Trailing zeros are significant only if there is a decimal present. Ex. 4.500 cm Ex. 300 4 sig figs 1 sig fig Ex. 4.50 x 10 5 3 sig figs note the exponent is not signficant 4. Leading zeros are not significant. Ex. 0.0056 Ex. 0.113 2 sig figs 3 sig figs
PRACTICE IDENTIFY THE NUMBER OF SIGNIFICANT FIGURES 1. 14.00809 2. 80,067 3. 0.0506 4. 4.67 x 10 5 5. 4,000,000 6. 5.00 x 10 5
ANSWERS TO PRACTICE QUESTIONS IDENTIFY THE NUMBER OF SIGNIFICANT FIGURES 1. 14.00809 7 sig figs (sandwich zeros) 2. 80,067 5 sig figs (sandwich zeros) 3. 0.0506 3 sig figs (sandwich zero is significant, leading zero not sig 4. 4.67 x 10 5 3 sig figs 5. 4,000,000 1 sig fig (trailing zeros, no decimal not significant) 6. 5.00 x 10 5 3 sig figs (trailing zeros with decimal, significant)
CALCULATIONS AND SIG FIGS Perform the math calculation as normal, round answer to correct number of significant figures. MULTIPLICATION AND DIVISION Round answer to the least number of sig figs. ADDITION AND SUBTRACTION Round answer to least number of decimal places.
CALCULATIONS AND SIG FIGS (CONT). MULTIPLICATION AND DIVISION Round answer to the least number of sig figs. Ex. 1 452 5 = 90.4 = 90 3 sig figs 1 sig fig answer must be rounded to least number of sig figs, 1 is less then 3, so final answer should be rounded to one sig fig 90 is one sig fig, the 0 is a trailing zero no decimal,so not significant Ex. 2 50.3 x.002516 = 0.1265548 = 0.127 3 sig figs 4 sig figs answer should be rounded to 3 sig figs
CALCULATIONS AND SIG FIGS (CONT). ADDITION AND SUBTRACTION Round answer to least number of decimal places, after the decimale. Ex. 1 250.879-25.1 = 225.779 = 225.8 places after decimal place after decimal round answer to least places after decimal, round to 1 place after decimal (tenths place) (thousandths place) (tenths place) Ex. 2 25.80700 + 14.23 = 40.037 = 40.04 5 places after decimal 2 places after decimal round answer to least places after decimal, round to 1 place after decimal (hundreths place) (hundred thousandths place) (hundreths place)
YOU TRY! Perform the following calculations and round your answer to the correct sig figs 1. 125 ml + 26.33 ml = 2. 46.88 x 12.0 = 3. 13.099-2.0 = 4. 300 14.69 =
ANSWERS Perform the following calculations and round your answer to the correct sig figs 1. 125 ml + 26.33 ml = 151.33 ml = 151 ml 2. 46.88 cm x 12.0 cm = 562.56 cm 2 = 563 cm 2 3. 13.099 g - 2.0 g= 11.099 g = 11.1 g 4. 300 m 3 14.69m = 20.42205582 = 20 m 2