 # Basic approximations in Python

Approximation means estimating the value of something that is not quite accurate, but almost correct. It plays a vital role in science and technology. Let`s start with the most common example. Have you ever used the exact pi value? Of course not. It is an infinite irrational number with a very long meaning. If we continue to write the exact value of Pi , perhaps even this article will not be enough for this:

` 3.14159 26535 89793 23846 26433 83279 ... `

So here where approximation plays a role. We usually approximate Pi as `3.14` or in rational terms `22/7` . When you got to high school, you probably saw a wider application of approximations in mathematics, which use differentials to approximate the values ​​of quantities, such as (36.6) ^ 1/2 or (0.009) ^ 1/3. In computer science, we can use approximation to find the value or approximate the value of something using loops.

For example: approximation of the cube root of any number. Take a look at the process below:

 ` # Python program to approximate ` ` # cube root of 27 ` ` guess ` ` = ` ` 0.0 ` ` cube ` ` = ` ` 27 ` ` increment ` ` = ` ` 0.0001 ` ` epsilon ` ` = ` ` 0.1 `   ` # Find an approximate value ` ` while ` ` abs ` ` (guess ` ` * ` ` * ` ` 3 ` ` - ` ` cube) & gt; ` ` = ` ` epsilon: ` ` guess ` ` + ` ` = ` ` increment `   ` # Check approximate value ` ` if ` ` abs ` ` (guess ` ` * ` ` * ` ` 3 ` ` - ` ` cube) & gt; ` ` = ` ` epsilon: ` ` ` ` print ` ` ( ` ` "Failed on the cube root of" ` `, cube) ` ` else ` `: ` ` print ` ` (guess, ` `" is close to the cube root of "` `, cube) `

Output of the above code:

``` 2.9963000000018987 is close to the cube root of 27
As we can see, 2.99 is not the exact value of ` (27) ^ 1/3 ` but is very close to the exact value 3. This is what we call approximation. Here we have used a series of calculations to approximate the value. First, we declare a variable ` guess = 0.0 ` which we will keep incrementing in a loop until it approaches the cube root of 27. Another variable ` epsilon ` is chosen as little as possible to get more accurate meaning. The line ` while abs (guess ** 3 - cube) & gt; = epsilon: ` will take care of this. If it breaks out of the loop with a value greater than ` epsilon `, it means that we have already crossed the approximate value and failed in the test. Otherwise, it will return the guess value.

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