Dealing with Data by Arthur J. Lyon and W. Ashhurst (Auth.)

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By Arthur J. Lyon and W. Ashhurst (Auth.)

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13-02, 1302,0-01302, and 13,020,000. On the other hand, 0-0020 has two significant figures but 20 and 2000 only have one. To avoid any ambiguity about the final zeros when there is no decimal point it is usual to write 1-302X107 instead of 13,020,000 and 2-3 X103 or perhaps 2-30X103 in place of 2,300. In the form 2-30X103 it is clear that there are three significant figures whereas the number 2300 would be assumed to have only two. It is also convenient to write 2-30X 10"6 in place of 0-00000230 to avoid writing too many zeros following the decimal point.

If this has the same maximum error of ±0-05 ml, determine x and its maximum error for this case also. Which measurement is the more precise? x = pN. (a) In the first case this gives 25x = 20-6X0-1 or x = 0-0824. The error ±0-05 in p is a relative error of 5/20-6%, or roughly 0-25%. The maximum error in x is therefore ±0-25x 0-0824/100 or ±0-0002 approximately. (b) Now we have 25JC = 2-1X1-0 or x = 0-084. The error of ±0-05 is now a relative error of 5/2-1% or roughly ±2-4%. The absolute error in x is therefore ±2-4X 0-084/100 or ±0-002.

C) 2-74 + 0-15. (d) (1-572 + + 0·052)Χ104. (e) (3-83±0-27)Xl0- 4 . (f) 7-82+0-074. ) t That is, where possible retain two uncertain digits in the result and two significant figure in the error estimate. CHAPTER 3 FREQUENCY DISTRIBUTIONS 15. THE FREQUENCY F U N C T I O N The experiments described in Chapter 1 showed that there are usually two elements present in the data occurring in the physical sciences—the controlled or systematic element and the uncontrolled, irregular, randomly fluctuating element.

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