Rounding decimals

When you re using repeating decimals in a problem, you decide how many decimal places you want and then round the number to that approximate value. Rounded decimals aren t exactly the same value as the repeating decimals, but you can make them pretty accurate in an application by using enough digits in the decimal equivalent. 

Naming Decimals Real-Life Decimals Rounding Decimals Comparing and Ordering Decimals... 

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 ... 

From Hilsenratb et al., N.B.S. Circ. 564, 1955. Some of the above values have been rounded to four decimal places. Values at 10-K increments below 1000 K and at 50 K increments for higher temperatures appear in the original, also for pressures below atmospheric. 

Example In an experiment, six random mimhers (rounded to four decimal places) were observed from the uniform distribiition /(A.) = 1 for 0 < a. < 1 ... 

The final tolerances the designer would allocate to the component dimensions are also shown in Figure 3.16. The tolerance values are given to three decimal places which, if required for practical use, can be rounded off with minimal effect to the overall assembly tolerance, for example 0.191 mm to 0.190 mm. 

Temperatures are average existing at 40 latitude and are rounded to even numbers. jNegative exponent shows number of spaces the decimal point must be moved to the left. Courtesy Ingersoil-Rand Co. 

Note that the 18.6 includes the reboiler, so physical trays in column = 17.6. Do not round-off decimal or fractions of trays until after efficiency has been included. 

Temperalures are average existing al 40° latitude and are rounded lo even numbers. jNegalive exponent shows number of spaces Ihe decimal point must be moved lo Ihe left. Courtesy Ingersoll-Rand Co. 

The second significant digit in (underlined) corresponds to the third decimal place of Xmean- In reporting this result, one should round as follows ... 

Correlation coefficient r or coefficient of determination (these indicators are not overly useful, see Section 2.1, but so well-known that some bureaucrats are unhappy if they do not have them, so they were included here but rounded to four or five decimal places). 

Note that a number of complicating factors have been left out for clarity For instance, in the EMF equation, activities instead of concentrations should be used. Activities are related to concentrations by a multiplicative activity coefficient that itself is sensitive to the concentrations of all ions in the solution. The reference electrode necessary to close the circuit also generates a (diffusion) potential that is a complex function of activities and ion mobilities. Furthermore, the slope S of the electrode function is an experimentally determined parameter subject to error. The essential point, though, is that the DVM-clipped voltages appear in the exponent and that cheap equipment extracts a heavy price in terms of accuracy and precision (viz. quantization noise such an instrument typically displays the result in a 1 mV, 0.1 mV, 0.01 mV, or 0.001 mV format a two-decimal instrument clips a 345.678. .. mV result to 345.67 mV, that is it does not round up ... 78 to ... 8 ). 

Comment The sequence of digits in each coefficient depends on the precision (e.g., three decimal places) and number of tabulated values (34, 50, or 64), the form of the optimization software used (Hewlett Packard HP71B Curve Fit Module), and the number of coefficients chosen (3. .. 8). Discrepancies between the approximated and the real table entries of up to j-LSD could be due either to insufficiencies of the algorithm or the rounding of table entries. The few LRR that are above 1% do not pose a risk for practical applications. 

Values of the spray volume and amount of test substance are rounded off to one decimal place. 

Notice how the lab value variable has been rounded to an arbitrary precision to the ninth decimal place. This gets around the floating-point comparison problem, while at the same time it avoids rounding the lab value variable to a precision where meaningful data are lost. 

If the first digit to be dropped is a 5, and there are no digits or only zeros after the five, we change the last digit remaining to the nearer even digit. The following numbers are rounded to one decimal place ... 

These 10 sets of problems will familiarize you with arithmetic operations involving decimals (which are a really special kind of fraction). You use decimals every day, in dealing with money, for example. Units of measurement, such as populations, kilometers, inches, or miles are also often expressed in decimals. In this section you will get practice in working with mixed decimals, or numbers that have digits on both sides of a decimal point, and the important tool of rounding, the method for estimating decimals. 

---