chem-201-chapter-3

chem-201-chapter-3 - 10/6/11 Significant Figures...

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10/6/11 1 Significant Figures When writing a number, it is important to know how well the value of the number is known. Examples If I say I have 12 donuts, I usually mean I have exactly 12 donuts because donuts do not come in fractions of a unit. Significant Figures If I say I have 12 grams of salt, does that mean exactly 12 grams or something between 11.5 and 12.5 grams. Because the mass of an object in grams may be expressed in fractions of grams, I must specify as precisely as possible what the mass is. Significant figures indicate the precision with which a number has been determined. Significant Figures When expressing a value, the number of digits used indicates the number of digits that could be measured accurately. The final digit in the value is an estimate of the least precise number. 4 6 5 Length = 5.73 units Significant Figures The manner in which a number is written indicates the number of significant figures it has. Examples 4000 1 significant figure the zeros are simply place holders and do not indicate precision of the measurement. in scientific notation: 4 x 10 3 Significant Figures 4000. 4 significant figures By placing a decimal point after the last zero, this indicates that the zeros were measured in scientific notation: 4.000 x 10 3 Significant Figures 4000.000 7 significant figures zeros following the decimal point with no other digits behind them also indicate precision of measurement, so they count as significant figures
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10/6/11 2 Significant Figures .0004 1 significant figure for numbers less than one, zeros following the decimal point, but before the first digit, are simply place holders and do not indicate precision in scientific notation: 4 x 10 -4 Significant Figures .000400 3 significant figures zeros following digits in numbers less than 1 indicate precision and are significant. in scientific notation: 4.00 x 10 -4 Mathematical Rules for Significant Figures Addition/Subtraction When adding or subtracting numbers, the number of significant figures in the result is determined from the position relative to the decimal point of the least significant figure of the numbers being added or subtracted Because 472.1 has only 1 sig. fig. after the decimal point, the final answer can have only 1 sig. fig. after the decimal point—the correct answer is 5476.2 Mathematical Rules for Significant
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chem-201-chapter-3 - 10/6/11 Significant Figures...

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