1.7:
Numerical Calculations
Engineering applications rely heavily on numerical calculations, whose results are represented in a standard format.
In numerical calculations, the equation must be dimensionally homogeneous, and the terms must be expressed in the same units.
The dimensional homogeneity of the equation is maintained regardless of the equation being assessed.
Numbers are rounded off to the required significant figures for the accuracy of the result; and are expressed in multiples of 103. If the number is less than one, the number is rounded off to the required significant figures and is expressed in the multiples of 10-3.
According to the rule, when a number ends with a digit greater than five, it is rounded up, and when the digit is less than five, the number remains the same, up to the significant figures.
When the number ends with the digit value five, it is rounded up only if the preceding number is odd, and if it is even, it remains the same up to the significant figures.
1.7:
Numerical Calculations
In engineering applications, the representation of the numerical value is critical. Presenting or reporting the answer is one of the essential parts of engineering practices. Numerical calculations are performed using handheld calculators or computers since numerically accurate answers are always preferred.
The solution to a problem is obtained using different methods. While manually solving algebraic symbols is one of the most common methods, the graphical method is often preferred. Computers come in handy when many equations are to be solved. A dimensionally homogeneous equation should be used while performing these calculations. Units used in such equations should be of the same system.
The accuracy of a numerical problem depends on several factors. How many significant figures are contained in any numerical value are one such factor. Since a whole number ending with zeroes always leads to confusion, the result is reported using engineering notation. Most of the values are expressed using prefixes.
Prefixes are always used to express large or small numbers. The result is rounded-off to the required significant numbers and expressed in multiples of (103).
Knowing how many significant figures should be used to express the numerical value is essential. For example, 34,600 can be expressed as 34.6(103) if three significant figures are required.
If five significant figures are required, the same number can be expressed as 0.34600(106).
In decimals, the beginning zeroes are insignificant; for example, the decimal 0.00456 has only three significant figures. If the number begins with zeroes, such numbers are expressed as 4.56 (10-3) or 456(10-6).
Too large and small numbers are rounded off to the required significant figures. However, while rounding off a number, the accuracy of the final result should remain the same. Almost all calculators are designed to round off the value. While performing the several steps, it is better not to round off the answer until the last step. Only the answer or the result should be rounded off based on the required accuracy. Most of the answers in engineering applications are expressed using three significant figures.
Leitura Sugerida
- Hibbeler, R.C. (2016). Engineering Mechanics ‒ Statics and Dynamics. Hoboken, New Jersey: Pearson Prentice Hall. pp 10‒11
- Beer, F.P.; Johnston, E.R.; Mazurek, D.F; Cromwell, P.J. and Self, B.P. (2019). Vector Mechanics for Engineers ‒ Statics and Dynamics. New York: McGraw-Hill. pp 13 and 15
- Meriam, J.L.; Kraige, L.G. and Bolton, J.N. (2020). Engineering Mechanics ‒ Statics. Hoboken, New Jersey: John Wiley.