Today, we have different number systems. Most students learn these number systems during their middle school. Some of these number systems are used frequently, and the others are rarely used. The number systems that middle students learn are Natural numbers, Whole Numbers, Integers, Rational Numbers, and Irrational numbers.
Natural numbers are the first numbers most people learn as they learn how to count numbers.
N = {1,2,3,4,5,6,7……..}
Natural numbers ranges from 1 to infinity. The space between the numbers is at least one.
Whole numbers are really simple if you know what Natural numbers are. Whole numbers are just Natural numbers plus 0.
W= {0,1,2,3,4,5,6,7….}
Whole numbers ranges from 0 to infinity, where the spaces between them is at least one.
Integers are easy to get, too. It is Natural number plus negative Natural numbers with zero.
I = {…-4,-3,-2,-1,0,1,2,3,4…}
Integer numbers ranges from negative infinity to positive infinity. The space between the numbers is at least one.
The definition of Rational number is any number that can be expressed in P/Q where P and Q are Integers. Therefore, all fractions are rational numbers. Also, Integers can be expressed in fractions as well. For Example
3 = 3/1 which can be expressed as a fraction. Therefore, all integers are Rational numbers.
Also decimal numbers that is finite is Rational numbers. For example,
0.8 = 4/5 which can be expressed in fraction. Therefore all finite decimal numbers are Rational numbers.
For infinitely long decimals, if it has repeating patterns, it is rational. If it does not have special patterns then it is not a rational number. For example,
0.345345345345345…. it has a special pattern of repeating 345s. and this can be expressed in fraction 345/999.
However,
0.141512352346264545… does not have any repeating patterns, so it is not a rational number.
The space between rational numbers is extremely close to zero; 0.1111111111 and 0.11111111110 has 0.00000000001 space in between them. Obviously, there are rational number with even smaller space.
Definition of Irrational number is simple. Irrational numbers are real numbers that are not rational.
Examples of Irrational numbers are π(pi) and (square root of 2). These numbers are infinite decimals with no repeating patterns.
Integers and Rational numbers are frequently used compared to Irrational numbers. However, it is important to know definitions of all number systems.
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This article was written for you by Edmond, one of the tutors with Test Prep Academy.