Cloud Computing in Engineering Workflows: Transforming Design, Collaboration, and Innovation In today’s fast-paced engineering landscape, the need for speed, scalability, and seamless collaboration is greater than ever. Traditional engineering workflows often relied on on-premises servers, powerful local machines, and fragmented communication tools. But as projects grow in complexity and teams become more global, these systems can no longer keep up. This is where cloud computing steps in—reshaping how engineers design, simulate, collaborate, and deliver results. What is Cloud Computing in Engineering? Cloud computing refers to the use of remote servers hosted on the internet to store, process, and analyze data. Instead of being limited by the hardware capacity of a single computer or office server, engineers can leverage vast, scalable computing resources from cloud providers. This shift enables engineers to run simulations, share designs, and manage data more efficiently. Key Be...
OPERATION OF NUMBERS
1.NUMBERS:
We have ten digits, namely 0,1,2,3,4,5,6,7,8,9. A number is denoted by a group of digits, called numeral. A numeral can be written in words by Units, Tens, Hundreds, Thousands, Ten-thousands, Lakhs, Ten-lakhs, Crores, Ten-Crores.
Eg: 581406099, can be written as fifty eight crores fourteen lakhs six thousand and ninety nine.
2. Face value and Place value of a Digit in Numeral:
Ex: 8421, the face value of 8 is 8, the face value of 4 is 4, the face value of 2 is 2, and the face value of 1 is 1.
Place value of 8 is (8*1000)
Place value of 4 is ( 4*100)
Place value of 2 is (2*10)
Place value of 1 is (1*1)
3. Types of Numbers:
*Natural Numbers: Counting numbers are called natural numbers (1,2,3,4,5,6,7,8,9...)
*Whole Numbers : Counting numbers and zero is a whole number (0,1,2,3,4,5,6,...)
*Integers : All counting numbers, zero and negative of counting numbers together for a Integers(.....-2,-1,0,1,2...)
4. Odd and Even Numbers:
*Odd Numbers: Numbers which are not divisible by 2 is odd number. Eg:(1,3,5,7,9...)
* Even Numbers: Numbers which are divisible by 2 is even number.
Eg:(0,2,4,6,8...)
5.Prime Numbers:
A number is called prime number when it has exactly two factors, namely 1 and itself.
Eg: 2,3,5,7,11,13,17...., These numbers are divisible only by 1 and itself.
The numbers which are not prime are called composite numbers.
4 ,the number 4 is divisible by 1,4 and 2 it has more than two factors hence it is called composite number.
6.Co Primes:
Two numbers a and b said to be co-prime when the H.C.F of two numbers is 1.
Eg: (2,3),(4,5),(7,9),(8,11)...
DIVISIBILITY OF NUMBERS
* A number is divisible by 2,if its unit digit is 0,2,4,6,8.
*A number is divisible by 3, when the sum of the digits is divisible by 3.
Eg: 321, the sum of the digits is (3+2+1=6), which is divisible by 3. Hence the number 321 is divisible by 3.
* A number is divisible by 4, the last two digits of the number is divisible by 4.
Eg: 436, the last two digits is 36,it is divisible by 4. Hence the number 436 is divisible by 4.
*A number is divisible by 5, when the unit digit is 0 or 5.
Eg: 420, 495 the last digit of two numbers is 0 and 5 hence both numbers are divisible by 5.
*A number is divisible by 8, if the last three digit is divisible by 8.
Eg: 89352, the last three digit is divisible by 8 hence the number 89352 is divisible by 8.
*A number is divisible by 9, when the sum of all digits is divisible by 9.
Eg: 965421, the sum of digits of a number is 27 it is a divisible of 9 hence the number 965421 is divisible by 9.
*A number is divisible by 11, when the sum of digits of odd places and the sum of digits of even places is either 0 or divisible by 11.
Eg: 49235417( sum of odd places=4+2+5+1=12)-(sum of even places=9+3+4+7=23)=11. Hence the number 49235417 is divisible by 11.