Playing With Numbers Class 8 Notes- Chapter 16

What is the General Form of Numbers?

If a two digit number pq needs to represented in general form, then

pq=10p+q

Divisibility by 9 and 3

If a number X has the sum of its digits divisible by 3 and 9, then the number is divisible by 9 and 3.

For example, let’s see the divisibility of the number 15287 by the number 3.

Let’s see the addition of the digits in the given number

1+5+2+8+7 =23 and the number is not divisible by 3. Therefore, 15287 is not divisible by 3

Let’s see another example of a three digit number 24x which is divisible by 9 and what is the value of x.

The addition of the digits 2+4+x=6+x should be divisible by 9 and this results in the values 6 + x =9 or 18 and since x is a single digit, therefore, 6 + x = 9, x= 3

Reversing the Digits in a number with 2 digits

Lets us assume a number ab in which a is in the tens place and b is in the units place. And then the representing numbers in general form results in ab=10a+b. Reversing the number will result in the form ba=10b+a. After adding the two number, we get :

(10a+b) + (10b+a)=11a+11b=11(a+b)

The given number is a multiple of 11.

Reversing the Digits in a number with 3 digits

The general form of a number of three digits is abc=100a+10b+c. After reversing, the number will be cba=100c+10b+a

  • If a>c, the difference between the numbers will be

(100a+10b+c)-(100c+10b+a)=99a-99c=99(a-c)

  • Similarly, if c>a, then the difference will result in 99(c-a)
  • If a=c then difference is 0

Important Questions

  1. Find out the value of y if 21y5 is divisible by 9 and y is a number
  2. Find out the value of z if 31z5 is divisible by 9 and z is a number
  3. Find out the value of x if 24x is divisible by 3 and x is a digit
  4. Find out the value of z if 31z5 is divisible by 3 and z is a digit

 

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