10/2/20151 Significant Figures CEC. 10/2/20152 Why we need significant figures In every measurement in a lab, there are inherent errors. No measurement.

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Presentation transcript:

10/2/20151 Significant Figures CEC

10/2/20152 Why we need significant figures In every measurement in a lab, there are inherent errors. No measurement can be known exactly. For this reason, when we write or use measurements, we must recognize the limitations of how well we know the measurement.

10/2/20153 What are significant figures? Significant figures are all of the digits in a measurement that are known with certainty plus the first digit that is uncertain. Example – in the measurement cm, the 165 is know with certainty and the 3 in the tenths position is uncertain.

10/2/20154 Rules for significant figures All non-zero figures are significant. Zeros between non zero digits are significant. Leading zeros are never significant. Trailing zeros are significant only if a decimal is present in the number.

10/2/20155 Rule for adding and subtracting In addition and subtraction, the sum or difference has significant figures only in the decimal places where both of the original numbers had significant figures. Ie cm cm = 15.3 cm

10/2/20156 Rule for multiplying and dividing In multiplication and division, the product or quotient cannot have more significant figures than there are in the least accurately known original number. That is, count the significant figures in each of the numbers being multiplied or divided and keep the least amount for the number of significant figures in the solution.

10/2/20157 Rules for rounding When rounding off, if the first number to be dropped is  4 or less – round down  6 or greater – round up  5 followed by non-zero numbers – round up  Exactly 5 – round to the nearest even number