Students have studied different kinds of numbers, for example, natural numbers, whole numbers, integers, and rational numbers. They may have likewise studied various fascinating properties about these numbers, discovering factors, multiples and the connections among them. Similarly, in this chapter, students can investigate the huge sort of numbers in detail. These thoughts can help the students in legitimising trials of divisibility. There are two exercises in this chapter that covers the subject of Playing with Numbers.
What is the General Form of Numbers?
If a two-digit number pq needs to represented in general form, then pq=10p+q
Numbers in General Form
A 2-digit number (ab) in its general form, is written as:ab = (10xa)+(1xb)
Reversing the 2-digit Numbers and Adding Them
When a two-digit number is reversed and then added with the number, the subsequent number is perfectly divisible by 11. Also, the quotient is equal to the sum of the digits.
Reversing the 2-digit numbers and Subtracting Them
When a two-digit number is reversed, and then the larger number is subtracted from it, the smaller number, the resulting number is effortlessly divisible by 9. Also, the quotient is equal to the difference between the digits of the number.
Reversing the 3-digit numbers and Subtracting Them
When a three-digit number is reversed, and the smaller number is subtracted from, the larger number, the resulting number is effortlessly divisible by 99. Also, the quotient is equal to the difference between the first and third digit of the selected number. If all of the combinations of a three-digit number are taken and added together, then the resulting number is perfectly divisible by 111.
Divisibility by 10
If the digit of a number is 0, then the number is divisible by 10.
Divisibility by 5
If the digit of a number is either 5 or 0, it is divisible by 5.
Divisibility by 2
If the digit of a number is 0,2,4,6 or 8, then it is divisible by 2.
Divisibility by 9
A number is divisible by 9 only if the sum of its digits is divisible by 9.
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