An Introduction to Approximation

What is approximation?

An approximation is nothing but anything which is intentionally similar but not exactly equal to something else or you can say that approximation is not exact but close enough to be used. Words like approximately, approximate and approximately are used especially in a technical or scientific context. It can also be abbreviated as approx. Approximate is an estimation of a number or rounding a number to its nearest place value.

The term approximation can also be applied to various types of properties, for example, value, quantity, image, a description that are nearly, but not exactly correct, similar, but not exactly the same as the original value.

Although the concept of approximation is mostly applied to numbers, sometimes it is also applied to such things in mathematical functions, physical laws, and shapes. In science, an approximation can also be used as a simpler process or model where the correct model is difficult to use.

There can be various types of approximation where it’s typed depends upon variable information, the degree of accuracy. Somehow an approximate model is used to make our calculations easier. The approximation can also be used where incomplete information prevents the use of exact representations.

The theory of approximation is also related to the branch of mathematics or a quantitative part of functional analysis. Approximation also arises naturally in Scientific experiments. The history of science proved that earlier laws and theories in science can be an approximation to some deeper set of laws. Sometimes the prediction of scientific theories and evidence can differ from actual sources and measurements because there are factors in the real situations that are not included in the theoretical sense. If we talk about the approximation of real number by rational numbers then Diophantine approximation is used.

Approximation mostly occurs when an exact form or any exact numerical number is unknown or difficult to obtain. The numerical approximation can also result from using a small number of significant digits. The results of computer calculations can also be approximation expressed in a limited number of significant digits. In terms of computer coding language, an approximation can occur when a decimal number cannot be expressed in a finite number of binary digits. But approximation usually come into existence in mathematical forms. Sometimes the known form of approximation may exist and may be able to represent its real form so that so significant derivation can be found.

The approximation can also be used where a number is not rational such as number ‘pie’, which is often shortened to 3.14159. Similarly, log tables, slide rules, and calculations produce approximate answers to all but the simplest calculations.

Examples of approximation

1- 214 rounded to the nearest tens is 210. As the digit in the ones place is less than 5, we round down the number to 0.

2- 4568 rounded to the nearest hundreds is 4600. As the digits in the hundreds place is 5, so we round up the number by adding 1 to that digit.

3- The chord measures 2.19, and you round it to “2”, as that is good enough.

4- 3.14 is an approximation of Pie(), which is actually 3.14159……….

5- The bus ride takes 58 minutes and you say it is ‘a one-hour bus ride’.

I hope, this article will help you a lot to understand the An Introduction to Approximation. If you still have any doubts and problems with any topic of mathematics you can ask your problem in the Ask Question section. You will get a reply shortly.

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