Irrational Numbers List

In the previous post we have discussed about Is 0 a rational or Irrational number and In today's session we are going to discuss aboutIn mathematics, any number written in the form of simple fraction is said to be irrational number or the number which is not rational is irrational number.

The ‘pi’ is the example of irrational number because its value after the decimal point is:

⊼ = 3.1415926535897……….. So it cannot be expressed in form of rational number.

Now we will see the irrational numbers list. The irrational number list is given below: A list of irrational numbers includes numbers like: (know more about Irrational Numbers List, here)

 √2, √3, √5, √7, √11, √13, √17, √19, √23, √29, √31, √37, √41, √43, √47, √53, √57, √59, √61, √63, √67, √69, √71, √73, √79, √83, √87, √89, √93, √97, √101, √103, √107, √109, √111, √113, √117, √119, √123, √129, √131, √137, √141, √143, √147, √153, √157, √159, √161, √163, √167, √171, √173, √173, √183, √187, √189, √193, √197, √201, √203, √207,√211………...and so on. The List of Irrational numbers include many other numbers. Let’s study some facts about irrational numbers:

·         Negative of an irrational number is also irrational number, meaning of this sentence is: if ‘y’ is irrational then ‘–y’ is also an irrational number.

·         If we add an irrational number and rational number then the sum we get is also irrational. Let ‘p’ is an irrational number and ‘q’ is a rational number then the sum (p + q) is also irrational.

·         In case of roots also the above step is applicable, let √7 is irrational and ‘e’ is rational then the sum √7 + e is also irrational. This is all about the irrational number list. Now we will Units of Momentum. Momentum can be defined as the product of mass and velocity of given object. The unit of momentum is kg.m/s. If you are prepression for IIT then please prefer online tutorial of iit sample papers. It is very helpful for iit exam point of view.   

Is 0 a rational or Irrational number

Before comparing that Is 0 a rational or Irrational number, it is necessary to learn about the rational and irrational. Rational number can be defined as a number which is written in the fraction form or written in p/q (in ratio). For example: 1.2 the number is rational because it is also written in the fraction form. So we can write it as 6/5. An irrational number can be defined as a real number which cannot be written in the fraction form or cannot be written in p/q form. For example: pi the value of pi is 3.14 it is not in the ratios. So pi is included in the categories of irrational number. In word we can say that the numbers are not rational are all irrational numbers.
Now we will see Is 0 a rational or Irrational number? According to the definition of rational number and irrational number we can easily say that ‘0’ is rational number because it can be written in the form of p/q or in form of fraction. If we write 0 in fraction form then we can write it as:
⇨ 0 / 1 = 0
We can easily compare any number using the definition of rational number and irrational number.  Suppose we have given some number 9.5, 5, 1.75, √2, 0.111, √3, √99, now find which number is rational number and which one is irrational number. (know more about Is 0 a rational or Irrational number, here)
According to the definition of rational number and irrational number we can easily compare the given number.
9.5 can be written as 19/2, so it is rational number. 1.75 can be written as 7/4 so it is also rational number. √2, √3 and √99 cannot be written in the fraction form so these numbers are irrational number. And 0.111 can be written as 1/9 so it is also a rational number. So this is all about the rational and irrational number.
Now we will see the Units of Density, unit of density is given as kg/m³. Before entering in the examination of 10^th class please focus on 10th maths question paper. It is very helpful for exam point of view and In the next session we will discuss about Irrational Numbers List. 

How to Find Percentage

In the previous post we have discussed about Proportions and In today's session we are going to discuss about Percentage, It defines how a number is present in form of fraction. It is define as a ratio that is based on the whole number. We can describe percentage as a value occurred on per 100. As the name describe per cent in which cent means hundred. In this blog we are going to know about how to find percentage. When we define any number in terms of percentage as 25% means 25 / 100 or 25 per 100. It also express the method of changing any percent value in the whole number.

We can easily express a number in form of percentage , first generate a fraction that have numerator as the value for which we want to calculate percentage and denominator define as the whole value and then multiply this fraction with 100 .It gives the percentage as if there is part x and its whole value is y then percentage is expressed as x / y * 100.

We can describe whole process of generating percentage in form of some steps as:

(1): Find the whole value

(2): define the portion for which percentage will be calculated.

(3): Generate the fraction

(4): calculate the percentage by multiplying the fraction value with the 100.

All the steps are described by an example as if the value is 25 and whole value is 50 than percentage is calculated as put the whole value and partition value in form of fraction as 25 / 50 and then multiplied it with 100 as 25 / 50 * 100 = 50 % that means 25 is 50 % of 50 that means 25 is just half of 50.

Cognitive Bias describe as a deviation in the judgment that is generate in specific situation. It is express as the inherent errors in thinking.

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Proportions

In algebra proportion is define as the special form used for comparison of two ratios . When we talk about the ratios it define as relationship between two or more things. But when we talk about the proportion it is the method of setting two ratios equal. We can say it in other words as when two ratios are equal to each other then their proportion are also equal. It is explained as 1 / 2 is equal to the 2 / 4 or 14 / 28.

Proportions is used when there is one part is missing in the given ratio as if a ratio is equal to other ratio means there proportion are equal then we can easily find the missing value. (want to Learn more about Proportions, click here),

As if there are two ratios a / b that is equal to x / y then these are stated as

a / b = x / y means these ratios have same proportions.

Sometimes values are missing from ratios but having the same proportion as x / 10 and 1 / 2 have these ratios are stated as x / 10 = 1 / 2, so for finding the value of x we use the proportion as

x = 10 * 1 / 2

x = 10 / 2 = 5.

We can also depict the proportion as the comparison that shows the relative relation between two or more things in terms of quantity , quality and any other sort of measurement.

Topic on How to Graph a Circle will describe all the methods of graphing a circle in easy manner.

icse sample paper that is provided by the icse board that helps the students to understand the pattern of paper come in the exam and In the next session we will discuss about How to Find Percentage. 

Consecutive Odd Integers

In the previous post we have discussed about How to solve Consecutive Integers and In today's session we are going to discuss about Consecutive Odd Integers. Let us first talk about the integers. The numbers which can be expressed in the form of the whole numbers and their additive inverse are called integers. All the integers can be expressed on a number line. A number line contains the series of all positive and negative numbers marked at the equal interval, where we could observe the number zero at the center, positive numbers at the right of the number line and negative numbers at the left of the number line.  Now we will learn about the Consecutive Odd Integers. By the consecutive numbers, we mean the numbers appearing one after another. Thus 1, 2, 3 . . .  are consecutive integers.  Now if we talk about the consecutive odd integers, we mean the series of odd integers which occur one after another but are odd.  So we say that the series of odd consecutive integers are 1, 3, 5, 7, 9 , . . . . . . etc.  In case of writing the series of odd integers in the form  of general series we will assume any number x. We know that 2 * x will always be the odd number. Now on another hand we say that if we add 1 to the odd number, it becomes the odd number. For this we say that the number 2x + 1 is any odd number. Now to write the series of the odd consecutive integers, we write 2x + 1, 2x + 3, 2x + 5, 2x +7 . . . . etc. (know more about Integer, here

 In order to learn about the Variance Calculator, we will visit online math tutor and learn more about the related topics. Central Board of Secondary Education Sample Papers is also available in all the subjects and they can guide us to understand the   pattern of the question papers in the previous years. It will guide the students to prepare for the fore coming examinations.

How to solve Consecutive Integers

Integers are the numbers which can be expressed in the series from minus infinite to plus infinite. Now let us look at the consecutive integers. Two integers which exist one after another when they are expressed on the number line are called consecutive numbers. If we have any number n, then the successor  and the predecessor of the number n forms the series of the consecutive numbers. So if we have n = 5, then we have n-1 = 5 – 1 = 4 and  n + 1 = 5 + 1 = 6. Thus the series 4 , 5 , 6  are called consecutive numbers.   There series of consecutive numbers can be used to solve many word problem related to linear equations.  In case we talk about any 3 consecutive integers, we say that series will be x, x + 1 and x + 2. On the other hand if we need to write the series of even numbers, then we know that each even number is the multiple of 2, so the first number will be 2 * x. (know more about Integers, here

Thus the series of consecutive integers will be  2x , 2x + 2, 2x + 4. Now we will assume the series of odd consecutive integer numbers. For this we will assume the first odd integer as  2x + 1. The next odd integer will be  2x + 3, 2x + 5. Thus the series of consecutive odd numbers will be  2x + 1, 2x + 3 and 2x + 5.
 If we have the problem that the sum of 3 consecutive integers is 36, find the integers. Then we will first assume the three numbers as x , x + 1 and x + 2. Thus we represent the sum as :
X + x + 1 + x + 2  = 36
Or 3x + 3 = 36
Or 3x = 36 – 3
Or 3x = 33
Or x = 33/ 3 = 11
SO  the three numbers are 11, 12 and 13.
 In order to learn How do you Find the Circumference of a Circle, we can take online help from math tutor and learn  the concepts in details. CBSE physics syllabus is also available online and we can download the curriculum for different grades from it and In the next session we will discuss about Consecutive Odd Integers.

Problem solving strategies

To become a better problem solver you need to analyze the problem in deep first and it require a systematic approach. Problem solving strategies requires practice, the more you practice, the better you get.
 Strategies of problem solving are:
1.      Look for the clues: In problem solving strategies, first read the problem carefully and underline the clue words. Look for the facts given and what do you need to find out.

2.      Make a plan: In strategies of problem solving, firstly set a plan. Or if you have done any problem like this before then do what you did.  You can use formulae, sketches, tables or any pattern.

3.      Now solve: In problem solving strategies, whatever plan you have thought of, just solve the problem according to it.

4.      Checking your answer: In strategies of problem solving, look over the solution. Check if it is the probable answer and also check for the units to be used in the answer.

In problem solving strategies, the first thing you do is looking for a clue, for which you need to a skills in solving problems and practice is most important here.
For example: In strategies of problem solving, if we are looking for clues in addition.
Then clues can be total, sum, in all, perimeter and so on.
Now in problem solving strategies, if you are looking for the subtraction clues, then they can be difference, exceed or how much more.
Similarly, in strategies of problem solving, if we are looking for the clues of multiplication, then you should look for the words: total, area, times, product, etc.
And in problem solving strategies, if you are looking for the clues related to division, then you should look for the words: distribute, quotient, average, share, divide,etc.


In strategies of problem solving, after all of the above points , one point which you need to remember is practice as much as you can to become a good problem solver.
In The Next Session We Are Going To Discuss Grade VI, Tools To Solve Problems.