Subtraction mathematical operation

Compare and contrast the multiplication/division significant figure rule to the significant figure rule applied for addition/subtraction mathematical operations. Explain how density can be used as a conversion factor to convert the volume of an object to the mass of the object, and vice versa. 

As a general rule, mathematical operations involving addition and subtraction are carried out to the last digit that is significant for all numbers included in the calculation. Thus, the sum of 135.621, 0.33, and 21.2163 is 157.17 since the last digit that is significant for all three numbers is in the hundredth s place. 

In addition to the measured values and the analytical values (e.g. content, concentration), latent variables are included in the scheme. Latent variables can be obtained from measured values or from analytical values by means of mathematical operations (e.g. addition, subtraction, eigenanal-ysis). By means of latent variables and their typical pattern (represented in chemometric displays) special information can be obtained, e.g. on quality, genuineness, authenticity, homogeneity, origin of products, and health of patients. 

Although blocks are used to identify many types of mathematical operations, operations of addition and subtraction are represented by a circle, called a summing point. As shown in Figure 6, a summing point may have one or several inputs. Each input has its own appropriate plus or minus sign. A summing point has only one output and is equal to the algebraic sum of the inputs. 

In Matlab the standard mathematical operators for addition (+) and subtraction (-) can be used directly with matrices. As with transposition, Matlab automatically calls the appropriate functions to perform the operations. ... 

In Excel, mathematical operations of one or more cells can be dragged to other cells. Since a cell represents one element of an array or matrix, the effect will be an element-wise matrix calculation. Thus, addition and subtraction of matrices are straightforward. An example ... 

Probability bounds analysis combines p-boxes together in mathematical operations such as addition, subtraction, multiplication, and division. This is an alternative to what is usually done with Monte Carlo simulations, which usually evaluate a risk expression in one fell swoop in each iteration. In probability bounds analysis, a complex calculation is decomposed into its constituent arithmetic operations, which are computed separately to build up the final answer. The actual calculations needed to effect these operations with p-boxes are straightforward and elementary. This is not to say, however, that they are the kinds of calculations one would want to do by hand. In aggregate, they will often be cumbersome and should generally be done on computer. But it may be helpful to the reader to step through a numerical example just to see the nature of the calculation. 

Units are a necessary part of the specification of a physical quantity. When physical quantities are subjected to mathematical operations, the units must be carried along with the numbers and must undergo the same operations as the numbers. Quantities cannot be added or subtracted directly unless they have not only the same dimensions but also the same units, for example ... 

The p in pH is a mathematical operator. We have been dealing with several operators, including addition, subtraction, and square roots. The p-function... 

For many mathematical operations, including addition, subtraction, multiplication, division, logarithms, exponentials and power relations, there are exact analytical expressions for explicitly propagating input variance and covariance to model predictions of output variance (Bevington, 1969). In analytical variance propagation methods, the mean, variance and covariance matrix of the input distributions are used to determine the mean and variance of the outcome. The following is an example of the exact analytical variance propagation approach. If w is the product of x times y times z, then the equation for the mean or expected value of w, E(w), is ... 

The propagation of error has been given for the subtraction of two numbers. In this section, the propagation of error for other mathematical operations is given. 

If you refer to the section on Accuracy you will notice in the first example given on relative error calculation that the numerator was only 2 SF (0.10) after the subtraction step. Therefore, the denominator was rounded off to 2 SF (12) and the answer was expressed as 2 SF. The division by 3 to get the mean does not limit the SF to one because the 3 is part of a mathematical operation and not an experimental value. Some sources specify rounding off during a calculation while others say it should be done only at the end. In the relative error calculation, the answer is changed by 0.02% if rounding off is done at the end as shown below ... 

Matrix algebra provides a powerful method for the manipulation of sets of numbers. Many mathematical operations — addition, subtraction, multiplication, division, etc. — have their counterparts in matrix algebra. Our discussion will be Umited to the manipulations of square matrices. For purposes of illustration, two 3x3 matrices will be defined, namely... 

To add or subtract measurements, first perform the mathematical operation, then round off the result to the least precise value. There should be the same number of digits to the right of the decimal as the measurement with the least number of decimal digits. 

The elementary mathematical operations are addition, subtraction, multiplication, and division. Some rules for operating on numbers with sign can be simply stated ... 

Modern software s controlled spectrophotometers allow not only acquisition and storage of registered spectra They are equipped in modules enable mathematical operation like addition, subtraction, multiplication as well as derivatisation. 

A high-level mathematical language, based on the main arithmetic operations and their physical interpretation in terms of the process plant, includes the following operations addition, subtraction, multiplication, division, substitution and removal. These mathematical operations correspond to reconfiguring of the plant modular system so that the external rank r and/or the internal rank (number of units) u and functions of the modules (the number n and the functionality F), change. Substitution of modules can be of two kinds with a new or with an existing module. It is an operation of consecutive removal of one and addition of another module. 

Compare and contrast the multiplication/division significant figure rule to the significant figure rule applied for addition/subtraction in mathematical operations. 

After numbers are obtained by a laboratory measurement, they are normally subjected to mathematical operations to get the desired final result. It is important that the answer have the correct number of significant figures. It should not have so few that accuracy is sacrificed or so many that an unjustified degree of accuracy is implied. The two major rules that apply, one for addition/subtraction, the other for multiplication/division, are the following ... 

Operations that one might desire to perform between sueh polynomials inelude the standard mathematical operations of addition, subtraction, multiplication and negation. Division has to be considered a little more carefully. For example multiplying two polynomials one of order 3 and one of order 2 gives as follows ... 

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