Degree Measure (Sexagesimal System)

Degree Measure


Look at the adjoining protractor in which a straight line AOB is divided into 180 small parts. Each part is a degree or 1°.


Protractor

The most common unit of measurement of an angle is the degree. The system of measuring angles in degrees, minutes, and seconds is called Degree Measure or Sexagesimal System.

Radian Measure (Circular System)

Radian Measure


In the circular system of measurement of angles, the unit of angle is radian (c). A radian, written as 1c is the measure of an angle subtended at the centre of a circle by an arc equal to the length of its radius r.

1 radian angle

By measuring we can get the value of 1c = 57.27° nearly.

Divisibility Rules

Divisibility Rules

 

To check whether a number is exactly divisible by 2, or 3, or 5, or 7, etc. we have to go through the actual division. But, it is time-consuming and tedious performing actual division all the time. There are certain rules for the test of divisibility of any number by 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, or 11 without performing the actual division. They are called divisibility rules.

Here are the divisibility rules of any number by 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, and 11.

Money Exchange

Money Exchange

 

In the world, each country has its own currency. For example, the Currencies of Thailand, UK, and Nepal are Bhat, Pound Sterling, and Rupees respectively. The values of the currencies of different countries are different. The exchange of a currency of a particular country with the currency of another country is called Money Exchange.


 

There are different rates for the selling and buying of foreign currencies. The bank or money exchanger makes some profit from the difference in selling and buying rates.

Irrational Numbers

Irrational Numbers


Define Irrational Numbers with Examples.

 

Definition: A decimal number which is non-terminating and non-recurring is called an irrational number. Irrational numbers cannot be expressed in the form of p/q where p and q are integers and q≠0. The square root of all non-square numbers, cube root of all non-cube numbers, etc. are all non-terminating and non-recurring decimal numbers, so they are irrational numbers. π(pi) also is an irrational number.

Quick Math Solver

Quick Math Solver


 

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Rational Numbers

Rational Numbers


What is a Rational Number?

 

The definition of a rational number is “A number which can be expressed in the form of p/q or fraction where p and q are integers and q ≠ 0 is a Rational Number.


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Examples of Rational Numbers

 

All the integers and decimal numberes can be expressed in the form of p/q or fraction of two integers. For example 0 = 0/1, 1 = 2/2, -2 = -4/2, 0.5 = ½, 1.25 = 5/4, 0.3333… = 1/3 etc. Therefore, 0, 1, -2, 0.5, 1.25, 0.3333… etc. are some examples of rational numbers



Rational numbers include all the integers on a number line along with the fractions between integers. Look at the number line given below.


Rational Number Line

The set of rational numbers is denoted by Q.

Q = {… -1, …, -¾, …, -½, …, -¼, …, 0, …, ¼, …, ½, …, ¾, …, 1, …}

 

Note:

-      There are infinitely many rational numbers between any two integers.

-      There are infinitely many rational numbers between any two rational numbers.

Integers

Integers


What is Integer?

 

The definition of integer is “Any counting number whether it is negative(-), positive(+) or zero(0) is an integer.”

 

The set of integers is an infinite set from both the sides and it is denoted by Z.

Z = {…… -5, -4, - 3, -2, -1, 0, 1, 2, 3, 4, 5 ......}

Prime or Composite?

Prime or Composite


What are Prime and Composite Numbers?

 

Answer:

A number which has only two factors is called a Prime Number and a number having more than two factors is called a Composite Number.


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For example,

2 has only two factors 1 and 2, so 2 is a prime number.

3 has only two factors 1 and 3, so 3 is a prime number.

5 has only two factors 1 and 5, so 5 is a prime number.

etc. But,

4 has three factors 1, 2, and 4, so 4 is a composite number.

6 has four factors 1, 2, 3, and 6, so 6 is a composite number.

8 has four factors 1, 2, 4, and 8, so 8 is a composite number.

etc.