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CHMB16H3 (16)
Chapter 4

CHMB16 Chapter 4

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Kagan Kerman

Chapter 3 Experimental ErrorSignificant FiguresSignificant Figures the minimum number of digits needed to write a given value in scientific notation without loss of precisionoZeros are significant when they occur in the middle of a number 10101 or at the end of a number on the righthand side of a decimal point 01060oThe last significant digit always has some associated uncertaintyoInterpolation estimate all readings to the nearest tenth of the distance between scale divisions on a 50mL burette which is graduated to 01mL read the level to the nearest 001mLSignificant Figures in ArithmeticAddition and Subtraction express all numbers with the same exponent and align all numbers with respect to the decimal point round off the answer according to the number of decimal places in the number with the fewest decimal placesoIf the numbers to be added or subtracted have equal numbers of digits the answer goes to the same decimal place integers are always exact as in any of the individual numbersExample 18998403218998403283798121795 since 83798 only has 3 numbers after the decimal point and rounding of the final answeroIf the first insignificant figure is below 5 we round the number downoIn the addition or subtraction of numbers expressed in scientific notation all numbers should first be expressed with the same exponentExample 1632 x 1054107 x 1030984 x 1061632 x 105004107 x 105984 x 1051151307 x 1051151 x 105Multiplication and Division we are normally limited to the number of digits contained in the number with the fewest significant figuresoExample 43179 x 1012 x 36 x 101916 x 106oThe power of 10 has no influence on the number of figures that should be retainedLogarithms and AntilogarithmsoIf n10a then lognaExample 2 is the logarithm of 100 because 100102 and the logarithm of 0001 is 3 because 0001103oIn the equation above the number n is said to be the antilogarithm of aExample the antilogarithm of 2 is 100 because 102100oA logarithm is composed of a characteristic and a mantissaCharacteristic the integer part whole numberMantissa the decimal partoNumber of digits in the mantissa of logxnumber of significant figures in xoNumber of digits in antilogx 10xnumber of significant figures in mantissa of x Example log5403 x 10872674Example 106142139 x 106
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