Quotients rounding

Multiplying or dividing Round the product or quotient so that it has the same number of significant figures as the least-precise measurement — the measurement with the fewest significant figures. 

Multiplication or division. The product or quotient should be rounded off to the same number of significant figures as the least accurate number involved in the calculation. Thus, 0.00296 x 5845 = 17.3, but 0.002960 x 5845 = 17.30. However, this rule should be applied with some discretion. For example, consider the following multiplication ... 

Some division problems could go on forever. Quotients like that can be non-terminating decimals or they can be repeating decimals. We ll learn more about those in Chapter 11. For now, we ll round our decimals to four places. Still remember how to round decimals ... 

Another two left over. No matter how many zeros we had, we will always add another 6 onto the end of our quotient and have two left over. We will round our decimal to four places. In other words, we will round to the nearest ten thousandth. 5.45666 has a 6 in the hundred thousandths place, so we must round up. 5.45666 to the nearest ten thousandth is 5.4567. 

In the partitive task that we have just described the number of recipients is the divisor and the portion of sweets is the quotient. It is the other way round in another kind of task which is called a quotitive task. Quotitive tasks are portion control tasks. In a quotitive task you decide that each recipient will get, say, 3 sweets and you go on doling out 3-sweet portions until you run out of sweets. So the greater the allotted portion of sweets the smaller will be the number of recipients fortunate enough to receive a portion. So the size of the portion is the divisor, and the number of recipients the quotient. 

What is the quotient of 83.4 2.1 when rounded to the nearest tenth ... 

With Hr defined as above, the rounding error in the difference quotient is dominated by the subtraction in the numerator of Eq. (6.B-3). GREGPLUS uses the estimate 6mS 6 ) for the rounding error of each numerator term, thereby obtaining the root-mean-square estimate... 

Although the porewater measurements have become somewhat discredited because of this failure to achieve a balance between predicted reaction rates and sedimentary concentrations, it may be that Sayles s conclusion about the importance of these reactions in near-shore and river-mouth sediments (where the bulk of particulate material from rivers is deposited) is correct. One could assess this possibility by comparing Mg/Al and K/Al quotients in these sediments with those measured in the particulate material of the rivers. It would require a lot of highly accurate determinations (to within a few percent) and an excellent year-round measure of the Mg/Al quotient in the river particulate material to compare with the sediment measurements. Probably for this reason, this research has not been attempted. 

However, since the least number of significant figures in the data is two in 0.0021, the product and quotient should be rounded to two significant figures. 

Figure 3.9 Mass-volume data for a sample of cooking oil. (a) The third column is the result of dividing the measured mass by the measured volume. All quotients are rounded to the number of significant figures justified by the data, (b) The slope of the line between any two points, A and B, on the line, Am/AV, is the density of the oil. Notice that the slope of the line of the plot in part (b) is the same as the mass/volume ratio in the third data column in part (a). 

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