Significant Figures CEC 11/28/2018

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. 11/28/2018

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 165.3 cm, the 165 is know with certainty and the 3 in the tenths position is uncertain. 11/28/2018

Rules for significant figures All non-zero figures are significant All trailing zeros before an understood decimal point are not significant unless indicated to be significant by the use of a bar. All leading zeros are not significant. Trailing zeros after a decimal point are significant. 11/28/2018

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. 12.57 cm + 2.7 cm = 15.3 cm 11/28/2018

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. 11/28/2018

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 11/28/2018