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There is a whole branch of mathematics that deals with the question and it is not possible to answer the question wholly here.
For some irrationals, such as roots of polynomials, it is often simple to use the Newton-Raphson method. For other irrationals, such as e, or pi or phi, there are convergent series that can be used.
For example, e = 1 + 1/1! + 1/2! + 1/3! + 1/4! + ... The sum of the first 5 ters is accurate to 99.6%.
or
pi = 4/1 - 4/3 + 4/5 - 4/7 + ... This series is excruciatingly slow but there are much faster alternatives.
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Why is the location of an irrational number an approximate location?
It is not! The square root of 2, for example, is irrational but you can always locate it exactly by using the diagonal of a unit square.
What is the approximate of each irrational?
Every irrational number can be represented by a non-terminating non-repeating decimal. Rounding this decimal representation to a suitable degree will provide a suitable approximation.
What is the sum of an rational number and irrational number?
An irrational number.
Which of the following numbers will produce an irrational number when added to?
When added to a rational number, any irrational number will produce an irrational number.also, when added to an irrational number, any rational number will produce an irrational number.
Why is 01001000100001000001000000100000001. an irrational number?
It is not an irrational number!
What is the cubic root of 231?
6.13579244 (approximate, this is an irrational number)
When do you need to approximate an irrational number with a rational value?
If the simplified form of an expression contains an irrational number and a numerical evaluation is required then it is necessary to use a rational approximation.
Why is the location of an irrational number an approximate location?
It is not! The square root of 2, for example, is irrational but you can always locate it exactly by using the diagonal of a unit square.
What is the approximate of each irrational?
Every irrational number can be represented by a non-terminating non-repeating decimal. Rounding this decimal representation to a suitable degree will provide a suitable approximation.
What is the sum of an rational number and irrational number?
An irrational number.
Is an irrational number plus an irrational number rational?
No. The sum of an irrational number and any other [real] number is irrational.
The sum of a rational number and an irrational number is?
The sum of a rational and irrational number must be an irrational number.
How do you express irrational number on a number line?
Simply plot the irrational number at it's approximate location on the number line and label the irrational number. For example, if you were to plot pi on the number line, you would plot it at about 3.14 and label it with "π" (the pi symbol, if it doesn't show up) Another example is if you want to plot the square root of 2 on the number line. You would plot it at around 1.414 and label it with "√2"
Is 3.56 an irrational number?
No, 3.56 is not an irrational number. 3.56 is rational.
Whether a rational number multiplied by an irrational number gives an irrational number?
rational * irrational = irrational.
Is negative pi rational or irrational?
-Pi is irrational, because it does not terminate or repeat. Whenever you multiply an irrational number by a rational number (-1), the result is an irrational number.
Can you reduce decimals?
No. A number in 'decimal' format is either exact or approximate; there is no reduction needed or possible. A 'decimal' may be approximate if it is irrational (for example, pi, 3.14159...) or repeating (for example, 1/3, which is 0.333333....).
