Is -8 Rational Or Irrational

The Real Number system

In math, numbers are classified into types in the Real Number system.
Number systems can be subsets of other number systems.
So, a number tin accept more than 1 type .

Clear as mud? ☺ Well, let's learn more to brand it clearer than that!

Natural numbers

When we first learned to count, we started with 1, 2, 3, four….and kept learning until nosotros got to the millions and trillions, correct? These counting numbers (1, two, 3, iv, 5, 10, 100, 1000, 1,000,000…∞) are called natural numbers.

Whole numbers

Did you detect something missing in natural numbers? Yes, the number 0! Skilful catch!Add together that to natural numbers (0,one,two,three……∞) and you have whole numbers!

And so, equally you can see, natural numbers are a subset of whole numbers.
Also, see how the numbers 1,2, three….are both natural numbers and whole numbers?
0 is only a whole number, and not a natural number.

Integers

Integers include all whole numbers (0) and also the negatives of the natural numbers: then (∞…,-four, -3, -ii, -1, 0, 1, 2, 3,4, …∞).

And then let'southward look at the pattern again –

All natural numbers are whole numbers and integers
All whole numbers are integers
Negative numbers are integers merely

Rational Numbers

These numbers include all the to a higher place (natural, whole, integers) PLUS some types of fraction/decimal .

And then, what makes a fraction/decimal rational?

A fraction x/y, where numerator 10 is an integer (…,-4, -3, -2, -ane, 0, 1, 2, 3,four,…) and denominator y is a natural number (1, 2, 3,4) is rational.

In the same way, a decimal that does not keep repeating (.eg. ¼ = 0.25, ¾ = 0.75) is also rational. These are also called terminating decimals.

And so rational numbers can await like this:

(∞…,-4, -3.5, -3, -2¾, -ii, -1½, -1, 0, 0.88, 1, 1¼, 2, 2.38, 3, 3.91, iv, 4¼, …∞)

Irrational Numbers

An irrational number is a existent number that cannot exist written as a simple fraction . In other words, it's a decimal that never ends and has no repeating pattern .

A decimal that keeps repeating is a good case of this.
The most famous example of an irrational number is Π or pi .
- Π is the ratio of a circumvolve's circumference to its diameter.
- While it can be approximated to 3.14159, the bodily value of Π merely begins with 3.14159. The concluding known record calculation of Π is up to 2.vii TRILLION digits!
- Call up also, these are never-ending digits, with no repeating blueprint .

Image source: Wikipedia

More important – Π = iii.14159 cannot be expressed as a fraction!
- 22/7 is an approximation that nosotros employ for calculations.
- Then Π cannot be expressed equally a fraction, decimal digits keep going forever and do not repeat in a pattern. This makes it an irrational number!
Some other good instance is √two or square root of 2.
- If you calculate its value, information technology approximates to i.4142135623730950…
- This too cannot be expressed as a fraction, then it'due south irrational
Other examples –√3, √5, √7, √11 and and then on…

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As co-founder of STEAMism and TimeforAI, Divya is a artistic force with a million ideas running through her caput at any single moment. She is motivated and curious - involving herself in multiple initiatives, including existence a VolunTeen at Thinkery Children's Museum and a Teen Court volunteer.. She loves fence, writing, learning, connecting to others, and mentoring.