density property of real numbers

In the previous post we have discussed about Decimal Place value and In today's session we are going to discuss about  density property of real numbers. As we all are very well aware from the concept of number system. Number system is a collection of all kinds of numbers that are part of mathematics. From those numbers, real number is one of them that deal with irrational numbers, fractional numbers and integers values. Here we are going to discuss about the density property of real numbers. Before understanding the concept of density property of real number we need to understand why we use it.

So answer is that properties with real numbers play an important role for solving various kinds of mathematical problems. Like in algebra real numbers property helps in solving algebraic equations in a understandable and easier manner.

Density property of real numbers are kind of property that tell us that there are infinite numbers are exists between two real numbers. In the simple mean we can say that density property of real numbers is a kind of property which shows that between any two real numbers there is some other numbers exists.

According to the standard definition we can say that density property can finds the infinite numbers that are lies between any two real numbers. Suppose there are two real numbers given that is 2 and 3. Now by using the concept of density property of real number we can say that there are infinite numbers are lies between them. Like 2.1, 2.2, 2.3, 2.4 and so on. (know more about density property of real numbers, here)

The concept of density property of real number also varies with the fractional numbers. It means to say that if we have two fractional value then there are infinite numbers also exists between the fractional value.

The concept of Van Der Waals Forces is used in physical chemistry which calculates the sum of attractive or repulsive force between the molecules. Students who are appearing in board exam then icse sample papers helps them for their exam preparation.

Decimal Place value

Decimal can be define as a mathematical fundamental concept that deals with the numbers of numerals system. Decimal can be defined as a point which is placed between the two or more digit value. Students who want to understand the concept of decimal, they first required to understand the concept of Decimal Place value. In mathematics, decimal position can be defined as a place of any number set through which the value of any number can be determined by their corresponding position. The number value which contains a decimal value within it then value of each number is very important.

In the normal form, each value of any number has their specific position or place value. Suppose we have a number 1234. Here the number 1234 has a specific number place value. The value 4 can be consider as unit value, value 3 can be consider in the position of tens, in the same aspect 1 and 2 can be consider as a place value of thousand and hundred position. (know more about Decimal Place value, here)

But when we put a decimal point between the digits of any number that has more then two digit into their value then place value of digits gets change into two categories. It means to say that right side digit of number has different place value and left side has different place value. Suppose we have number 123.456. Here we can see that there is a decimal point between the number values and both sides have different place value. Here left side of decimal value remains as like normal number value but right side has different place value.

After decimal first digit can be consider as a tenths place value means 4 tenths. In the same aspect the value 5 and 6 after decimal point can be consider as a fifth hundredths and sixth thousandths. Surface Area of Cone can be calculated by using the following formula that are given below:

Surface Area of Cone = pi * r * s + pi * r * r

icse board stands for Indian Certificate of Secondary education that conducts national level board examination for class 10th and 12th. In the next session we will discuss about Comparing Fractions. 

Comparing Fractions

In mathematics, fraction can be defined as a ration representation of two whole numbers. Fraction is a part of number system that helps the students for resolving various kinds of mathematical problem. Fraction is most important mathematical concept that performs the task of expressing any number into ‘n’ number of equal parts. Suppose there is pizza which is required to be distributed between three friends. At that time the concept of fraction resolve the problem by distributing the pizza equally through which each friend get one- third part of pizza to eat.

In the concept of fraction, we perform the representation of two whole numbers in role of dividend and divisor. Like 2 / 3 and 4 / 5. Here the value 2 and 4 can be consider as dividend known as numerator for fraction and 3 and 5 can be consider as divisor known as denominator for fraction number. (know more about Comparing Fractions, here)

Here we are going to discuss about one of the fractional concepts which is popularly known as comparing fraction. As a name specified as comparing fraction is task of performing a comparison between the two fractional values.

It means to say that Comparing Fractions is to calculate which number is greater and which is lower. The comparing fraction can be performed by using some symbol like <, > and =. To perform the comparing fraction successfully between fractional values can be done by following some step that is given below:

Step a) First we need to calculate LCD.

Step b) When we perform the step A then we need to calculate the product of LCD value with top and bottom value of fraction number for equalizing the denominator value of both fractional number.

Step c) In the last step perform the comparison of numerator value and put the respective sign between them.

Surface Area of a Prism in rectangular form can be calculated by using following formula

2 * length * width + 2 ( length + width ) height

For board examination icse guess papers 2013 guide the students to make their exam preparation better. In the next session we will discuss about Decimal Place value.