MATHEMATICS : Number and Numerations
Welcome, in this class, I am going to put you through the definition of numbers and numerations and also list the various types of numbers with brief explanation. You are expected to answer the classwork’s questions so as to prove that you understood the topic properly.
What are Numbers and Numerations?
Numbers are arithmetical value, expressed by a word, symbol, or figure, representing a particular quantity and used in counting and making calculations and for showing order in a series or for identification.
Numeration is the process of calculating or assigning a number to something. For example, X= 5.
Below is the list of the various types of numbers;
Whole Numbers: these numbers are integers which are non-negative. The set of whole numbers is denoted by W. For example, W= {0,1,2,3,4,5,6,7,8,9,10,11,12,..}.
Natural Numbers: these are positive whole numbers. They are used for counting natural objects and are most times referred to as counting numbers. The set of natural numbers is denoted by N. For example, N= {1, 2, 3, 4, 5, 6, 7, 8, …}. Note: the number zero (0) is not included in Natural Numbers because it has no value when counting.
Negative Numbers: these are numbers that are less than zero and have a negative sign before them. They are usually at the left hand side of the number line and they are sometimes referred to as Negative integers. For example, (…,-5,-4,-3,-2, -1).
Integers: these are numbers that do not involve fraction and includes both Zero, Negative numbers and positive numbers. The set of integers is denoted by Z. For example, Z= {…,-3,-2,-1, 0, 1, 2, 3, 4, 5, …}.
Rational Numbers: these are the numbers that can be used to form a fraction or could be expressed as ratios. The set of rational numbers is denoted by Q where Q = {a/b: a, bє z, b≠ O}. For example, if we have 4/9, it implies that 4 and 9 are rational numbers.
Irrational Numbers: these are numbers that cannot be used to form a fraction. The set of irrational numbers is denoted by Q′. Examples of irrational numbers are ∏, e, and all surds. √2 is an irrational number therefore the √2 = 1,414…, but the square of 1.414 cannot give the exact value of 2 but only an approximated value.
Real Numbers: this is the combination of both the Natural, Whole, Rational, Irrational, Negative Numbers and Integers. It is denoted as R = W U M U Z U Q U Q′.
Imaginary Numbers: these are numbers believed to exist through imagination which we cannot simplify further. For example, √-1 and i is always assumed to be equal to √-1 (i=√-1 ) to make work easier. So, √-9 = √-1 x 9 =√-1 x √9 = 3i.
Complex Numbers: these are of the form a + ib, where a, b є R and i = √-1. Every complex number has both the real part and the imaginary part. The real part is a, while the imaginary part is ib. Complex number is denoted by C where C = {a + ib: a,b є R, i = √-1}.
Prime Numbers: these are natural numbers that cannot by any other number aside itself and 1. A prime number must have two factors; itself and 1. There 1 is not a prime number because it has only 1 factor –itself. The set or prime numbers is denoted by P. For example, P= {2, 3, 5, 7, 11, 13, 17, 19, 23,…}.
Even Numbers: these are numbers when if divided by 2 will leave no remainder. For example, {2, 4, 6, 8, 10, 12, 14, 16, 18, 20,…}.
Odd Numbers: these are numbers that cannot be divided exactly by 2 because they must leave a remainder. For example, 9/2 = 4.5.
Classwork
- List the whole numbers between 30 and 50.
- Give 3 examples each of an even number and prime number.
- In your own understanding, what do you think are irrational numbers?
- Identify the real and imaginary part in the following complex numbers (a)6 + 9i (b) -4 + 23i (c) 15i + -6
Until next time, goodluck.
Click here to download “MATHEMATICS : Number and Numerations” as PDF.
Click here to save this Post as PDF
