Rounding-off rules

Different rounding-off rules are needed for addition (and its reverse, subtraction) and multiplication (and its... 

Know how to determine the number of significant figures in a number, the rules for how many significant figures are to be shown in the final answer, and the round-off rules. 

Sometimes when you add, subtract, multiply, or divide experimentally measured quantities, the result contains digits that are not significant. When this happens, the result must be rounded off. Rules for rounding are as follows ... 

Step 3. Refer to Figure 4-7 and select an efficiency at a pressure ratio of 3 and a volume ratio, r of 2.44. The adiabatic efficiency is 74%. Now, from Figure 4-5, select a value of efficiency ratio using the tip speed ratio just calculated. Because the value is. 99+, round off to an even 1.0. With a multiplier of 1.0, the final adiabatic efficiency is the value read directly off the curve or T a = 74. The molecular weight correction for efficiency, per rule of thumb, is 0.6 for a final efficiency of 73.4. 

The rules for rounding off a measurement, which were applied in Example 1.3, are as follows ... 

We have seen that we must sometimes reduce the number of digits in our calculated result to indicate the accuracy of the measurements that were made. To reduce the number, we round off numbers other than integer digits using the following rules. 

For rounding off digits in any whole number place, use the same rules, except that instead of actually dropping digits, replace them with (nonsignificant) zeros. For example,... 

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 ... 

When calculations by a computer or by hand produce more figures than needed, they are rounded off to the proper number of significant figures. Laboratories commonly use the following rules for rounding off ... 

Example 4.8 illustrates the rules for rounding off and the significant figure determination. 

In propagating errors it is generally advisable to keep one or two extra digits in intermediate results, and round off only when you get to the final result. Applying this rule to the solubility product measurement, the mass of dissolved silver chloride is 0.888 0.0142 mg, and the formula weight of silver chloride is 143.3279 0.00042 g- mol"1. 

There are four rules for rounding off significant figures. 

According to the rule given in Step 6 in Table 7.12, there is no need to round off the reactor length. 

In most calculations you will need to round off numbers to obtain the correct number of significant figures. The following rules should be applied for rounding. 

Finally, a rule of thumb for rounding off numbers in which the digit to be dropped is a 5 is always to make the last digit of the rounded-off number even ... 

A rule of thumb that is sometimes suggested for multiplication and division is to round off the answer so that it contains the same number of significant digits as the original number with the smallest number of significant digits. Unfortunately,... 

In the three simple arithmetic operations we have performed, the number combination generated by an electronic calculator is not the answer in a single case The correct result of each calculation, however, can be obtained by rounding off. The rules of significant figures tell us where to round off. 

Rounding off according to the rules for significant digits, the molar mass ofPb(N03)2 = 331.2 g. 

Rounding off an answer that is derived from a mixture of subtraction (or addition) and division (or multiplication) is more complex than when these calculations are done separately. We need to recognize the different components of the problem and follow the proper rules for each. 

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