Multiplication of a Number by 5ⁿ-

Multiplication is the part of mathematics and Mathematics is a Greek word derived from the word “mathema”, which means knowledge. This study is related to different wings of mathematics involving number theory, algebra, and various analyses based on mathematics. The great mathematician Archimedes is known as the father of mathematics, he devoted his life to recognizing various aspects of mathematics. The development of every single thing in the world is based on the concept of multiplication and mathematics. The mathematics of several unique numbers can be identified easily like the multiplication of numbers with 5ⁿ.

Main body 

Multiplication 

Multiplication is known as one of the four elements of addition. The multiplication is also known as the product, the product is the result of multiplying two or more numbers. If the multiplication is made in the same number then it can be considered the copying of numbers. Mathematics is the process of calculating the results when two or more numbers are multiplied and the product is obtained. Suppose there are two numbers 5 and 6, when they are multiplied (5 x 6 = 30) the product is formed as 30. The 5 and 6 are the factors that are multiplied for getting the results or the products. The multiplication is represented by the sign “x”, used in representing the multiplication done between the two or more factors. The multiplications are of three types “Associative, Commutative, and Distributive”, all these multiplications are binary operations.  

The associative multiplication is one in which the multiplication of elements follow the following condition of a binary operation, “X*(Y*Z)= (X*Y)*Z”. 

Commutative multiplication is that multiplication with a binary operation, which satisfy the condition of multiplication of two numbers in form of “X*Y=Y*X”.  

Based on the different patterns of multiplication distributive multiplication is also considered with the pattern satisfying the multiplication as “(X+Y)Z=XZ + YZ”. 

Multiplication is one of the basic pillars of mathematics and it can be seen in different regions where the repetitive addition or other functions of mathematics is involved. The multiplication can be in the form of power, where the numbers are multiplied repeatedly and it can be considered as duplicate numbers. 

Multiplication of a Number by 5ⁿ 

The multiplication of any number with 5 or the number with unit digit 5 is considered in this condition. The multiplication of the various numbers with 5ⁿ can be seen in the different parts with results easy to identify. There are several conditions in multiplying any numbers with 5, the products of factors multiplied by 5 either give the result with the unit digit 5 or 0. The unit digit of the products is dependent on what kind of number is multiplied by the 5, whether it is even or odd. If 5 is multiplied by any even numbers the product will be with the unit digit zero 0 and if 5 is multiplied by any odd numbers then the unit digit of the product will be 5. If any of the factors has the unit digit 0 then the products multiplied will always have 0 in their unit digit.

Supposes there are two numbers 6 and 10, and then the product formed after multiplication will be-

“6*10 = 60”.

 The number formed after multiplication will be 60 with unit digit 0 in the product. 

Let’s take another case where there are also two numbers 25 and 3. The one factor other than numbers with the unit digit 5, which is 3 an odd number. Then the results of multiplication will be- 

“25*3= 75”

From the result or the product, it can be seen that the number is with the unit digit 5.

Take another sample of multiplications where one of the numbers is with the unit digit 5 and the other is an even number. Let the numbers be 45 and 12, then the product of the multiplication will be- 

“45*12= 540”

The number obtained as the product is 540 with unit digit 0 because unit digit 5 multiplied by the even number.  

Process to find Multiplication of a Number by 5ⁿ 

In the multiplication of any numbers with 5ⁿ, the same condition is applied as described in the above proportion. The “n” in 5ⁿ represent the power of the 5 for the multiplication process and “n” can be greater than zero but not equal to 0. n ≠ 0, n>0. If number 2456, is multiplied by 5ⁿ with n value 4 then 4 zeros are added with the place of 2456 as, 24560000. Then divide the whole 24560000 by the 2 with power n and the value of n = 4. 

“24560000/2n” = “2456000/16” =1535000

Conclusion 

The products are the results that are achieved by the multiplication of different numbers and any numbers which are multiplied by the 5 are easy to identify having a unit digit either 0 or 5. The relation o0f 5 and 0 can be seen in the methods used for the multiplication of any number with 5ⁿ. The relation between the 5ⁿ and 2 can be seen in the multiplication process, by dividing the whole numbers by 2n after adding n number of zeros in their unit place.