# Division by 10 and 100 and 1000

Division by 10 and 100 and 1000 are explained here step by step. We know the following facts regarding division process:

1. (i) When any number is divided by 1, the quotient is the number itself.

(a) 7 ÷ 1 = 7

(b) 53 ÷ 1 = 53

(c) 275 ÷ 1 = 275

(ii) When a number (except 0) is divided by itself, the quotient is 1.

(a) 7 ÷7 = 1

(b) 53 ÷ 53 = 1

(c) 275 ÷ 275 = 1

(iii) When zero (0) is divided by any number, the quotient is zero (0), but no number can be divided by zero (0).

(a) 0 ÷ 8 = 0, 0/8 = 0, 0 ÷ 115 = 0, 0/115 = 0

(b) 0 ÷ 0 has no meaning, 10 ÷ 0 has no meaning, 15 ÷ 0 has no meaning.

2. When a number is divided by 10, the digits, except the digit at the one's place, make the quotient and the digit at one's place becomes the remainder.

As for example:

(i) 48 ÷ 10 Quotient = 4 Remainder = 8

(ii) 76 ÷ 10 Quotient = 7 Remainder = 6

(iii) 492 ÷ 10 Quotient = 49 Remainder = 2

(iv) 178 ÷ 10 Quotient = 17 Remainder = 8

(v) 569 ÷ 10 Quotient = 56 Remainder = 9

(vi) 4183 ÷ 10 Quotient = 418 Remainder = 3

(vii) Divide 84 by 10.

Solution:

(vii) Divide 868 by 10.

Solution:

Thus, when a number is divided by 10, the remainder is always the digit of the unit place and the quotient is the number made by the remaining digits.

In other words, when we divide a number by 10, the digit at ones place of the given number becomes the remainder and the digits at the remaining places of the number given the quotient.

Therefore, notice that on dividing by 10, the digit in the ONES place forms the remainder, while the remaining digits form the quotient.

3. When a number is divided by 100, the quotient is the number made by the digits, except the digits at one's and ten's places. The number formed by ten's and one's digit of the dividend number is the remainder.

As for example:

(i) 476 ÷ 100

Will give quotient 4 remainder 76

(ii) 3479 ÷ 100

Will give quotient 34 remainder 79

The number of digits in the remainder is equal to the number of zeros in the divisor.

(iii) 527 ÷ 100 Quotient = 5 Remainder = 27

(iv) 609 ÷ 100 Quotient = 6 Remainder = 9

(v) 7635 ÷ 100 Quotient = 76 Remainder = 35

(vi) 7635 ÷ 100 Quotient = 30 Remainder = 79

(vii) Divide 396 by 100.

Thus, when the dividend number is divided by 100, the extreme right two digits form the remainder and the rest of the digits form the quotient.

In other words, when we divide a number by 100, the digit at ones and tens place together of the given number forms the remainder and the digits at the remaining places of the number given the quotient.

Therefore, when we divide by 100, the two digits in the ONES and the TENS place form the remainder while the remaining digits form the quotient.

4. Following this method, when we divide by 1000, the remainder will have 3 digits.

When a number is divided by 1000, the quotient is the number made of the digits except the digits at one's, ten's and hundred's place. The number formed by these three digits is the remainder.

As for example:

(i) 1379 ÷ 1000

Will give quotient 1 remainder 379

(ii)45362 ÷ 1000

Will give quotient 45 remainder 362

The 3 digits in the ONES, TENS, HUNDREDS places form the remainder.

(iii) 3851 ÷ 1000 Quotient = 3 Remainder = 851

(iv) 9874 ÷ 1000 Quotient = 9 Remainder = 874

(v) 35786 ÷ 1000 Quotient = 35 Remainder = 786

(vi) Divide 4129 by 1000.

Solution:

Thus, when the dividend number is divided by 1000, the extreme right three digits form the remainder and the rest digit/digits form the quotient.

In other words, when we divide a number by 1000, the digit at ones, tens and hundreds place together of the given number forms the remainder and the digits at the remaining places of the number given the quotient.

Division of a number by 20, 30, 40.....

(i) 80 ÷ 20

20 × ____ = 80

2 × 4 = 8

So, 20 × 4 = 80

(ii) 140 ÷ 70

70 × ____ = 140

7 × 2 = 14

So, 70 × 2 = 140

(iii) 900 ÷30

30 × ____ = 900

3 × 3 = 9

30 × 3 = 90

So, 30 × 30 = 900

(iv) 320 ÷ 80

80 × ____ = 320

8 × 4 = 32

So, 80 × 4 = 320

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