Irrational Number Definition

By Author: Pierce Brosnan
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Introduction irrational numbers:

Irrational numbers in difference to rational numbers are not presented a fraction of the shape:`(m)/(n)`, where m and n are integers. There are numbers of a new type, which are calculated with any accuracy, but cannot be changed by a rational number. They can appear as outcome of geometrical measurements.

More about irrational fraction

Types of fraction:

It is very important and types of fractions.

Proper fraction

Improper fraction

Mixed fraction

An integer is any whole number (positive or negative) (e.g. -176, -3, 0, 85, 1633).

An integer cab is positive (e.g. 1,8,21,154);

An integer cab is negative (e.g. -45,643,-2091,-55) or

An integer cab is zero (0) which is neither positive nor negative.

Consecutive integers are integer values that follow each other sequentially by adding 1 to the pervious integer value.

For example:

5 consecutive integers starting at 14 are: 14, 15, 16, 17 and 18. If t he starting integer is -3, then 5 consecutive integers are: -3, -2, -1 and 1.

In general, the following ...
... formula applies to consecutive integers where n is any integer (positive, zero or negative): n, (n+1), (n+2), (n+3), (n+4), etc.

Consecutive positive integers includes only positive integers (e.g. 7, 8, 9, 10, etc.)

Consecutive positive integers includes only negative integers (e.g. -11, -10, -9, -8, etc)

Consecutive positive integers includes only sequential odd integers (e.g. 7, 9, 11, 13, 15, etc.)

Consecutive positive integers includes only sequential even integers (e.g. 24, 26, 28, 30, etc.)

Where can you find special irrational numbers?

The answer to this depends on what you consider 'special'. Mathematicians have proved that definite special numbers are irrational, for example Pi and e. The number e is the base of natural logarithms. It is irrational, just like Pi, and has the value 2.718281828459045235306....

It is not easy to just "come up" with such special numbers. However, you can easily discover more irrational numbers after you have found that most square roots are irrational. For example, what do you think of ?2 + 1? Is the result of that addition a rational or an irrational number? How can you know? What about other sums where you add one irrational number and one rational number, for example ?5 + 1/4?

You can also add two irrational numbers, and the amount will be many times irrational. Not always though; for example, e + (-e) = 0, and 0 is rational even though both e and -e are irrational. Alternatively, take 1 + ?3 and 1 - ?3 and add these two irrational numbers - what do you obtain?

Alternatively, increase/separate an irrational number by a rational number, and you get an irrational number. For example, ?7/10000 is an irrational number that is moderately close to zero. Yet another possibility to discover irrational numbers is to multiply square roots or other irrational numbers. Sometimes that outcome in a rational number though (when?). Mathematicians have also calculated what happens if you raise an irrational number to a rational or irrational power.

Yet more irrational numbers begin when you take logarithms, or calculate sines, cosines, and tangents. They do not have any particular names, but are just called "sine of 70 degrees" or "base 10 logarithm of 5" etc. Your calculator will give you decimal approximation to these.

Examples of Irrational number:

`Pi` , ?10 Are few examples of irrational numbers.

Solved Example on Irrational Number

Identify the irrational number.
Choices:
A. 0.3
B. 3 / 5
C. ?6
D. ?25

Correct Answer: C

Solution:

Step 1: The value of is 2.4494897427831780981972840747059...

Step 2: The value of is 5.

Step 3: The value of is 0.6.

Step 4: Among the choices given, only is an irrational number

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