The distance of a number from a convenient round number(base) or how far the number is from its base is known as the complement of a number.

Numbers such as 10,100,1000 are usually taken as bases as they are friendly numbers.

It is a simple concept but very helpful when you apply this concept to solve problems.

Suppose you want to substract two difficult numbers then if you know the complement of the numbers then you will be surprised to see how quickly you can mentally calculate the answer.

Let us now find out the complements of numbers taking different bases.

First lets start finding complement of numbers from 1 to 9 with 10 as base

10-1=9

9 is a complement of 1

10-2=8

8 is a complement of 2

10-3=7

7 is a complement of 3

10-4=6

6 is a complement of 4

10-5=5

5 is a complement of 5

10-6=4

4 is a complement of 6

10-7=3

3 is a complement of 7

10-8=2

2 is a complement of 8.

10-9=1

1 is a complement of 9.

Now lets take the base as 100 and find complements of numbers

To find the complement of a number with 100 as base follow the below steps

For the unit’s place digit find the complement of the units place digit with 10 as base

For the ten’s place digit find the complement of the ten’s place digit with 9 as base

We shall now practice few examples to perfect the skill that we learnt

100-11=?

Steps

For the unit’s place digit find the complement of 1 with base 10 (10-1=9)

For the ten’s place digit find the complement of 1 with base 9 (9-1=8)

Ans 100-11=89

100-21=?

Unit’splace digit=Complement of 1 with base 10 is 9(10-1=9)

Ten’s place digit=Complement of 2 with base 9 is 7(9-2=7)

Ans 100-21=79

100-42=?

Unit’splace digit=Complement of 2 with base 10 is 8 (10-2=8)

Ten’s place digit=Complement of 4 with base 9 is 5 (9-4=5)

Ans 100-42=58

Now lets take the base as 1000 and find complements of numbers

To find the complement of a number with 1000 as base follow the below steps

For the unit’s place digit find the complement of the units place digit with 10 as base

For the ten’s place digit find the complement of the ten’s place digit with 9 as base

For the hundreth’s place digit find the complement of the hundreth’s place digit with 9 as base

We shall now practice some examples

1000-121=?

Unit’splace digit=Complement of 1 with base 10 is 9 (10-1=9)

Ten’s place digit=Complement of 2 with base 9 is 7 (9-2=7)

Hundreth’s place digit=Complement of 1 with base 9 is 8 (9-1=8)

Ans 1000-121=879

1000-472=?

Unit’splace digit=Complement of 2 with base 10 is 8 (10-2=8)

Ten’s place digit=Complement of 7 with base 9 is 2 (9-7=2)

Hundreth’s place digit=Complement of 4 with base 9 is 5 (9-4=5)

Ans 1000-472=528

Note

If the unit’s place is 0 then Ignore the 0 and start finding the complement of the number from the next digit.

For example lets say we want to find the complement of 220

1000-220=?

Unit’s place digit=0

Ten’s place digit =Complement of 2 with base 10 is 8 (10-2=8)

Hundreth’s place digit=Complement of 2 with base 9 is 7 (9-2=7)

Ans 1000-220=780

1000-470=?

Unit’s place digit=0

Ten’s place digit =Complement of 7 with base 10 is 3 (10-7=3)

Hundreth’s place digit=Complement of 4 with base 9 is 5 (9-4=5)

Ans 1000-470=530