In this section, we are going to study multiplication with special numbers – repeating numbers.

Repeating numbers are those numbers whose digits are repeated in a unique pattern. For example – 101, 202, 103, 1001, 10003, 10101, 1020 etc.

Multiplying any number with these repeating numbers is very simple, if we know the right technique to use. This is more useful when the number being multiplied has less digits than the digits in repeating number. However, it can be extended to other numbers also and we have to deal with carries in such cases. We will study all these cases with the help of examples.

For example:

34 x 101 = ?

This multiplication can be seen in 2 parts:

34 x 100 + 34 x 01 = 3434, as 101 = 100 + 1;

repeating-1

Let us see another example:

432 x 1001 = ?

repeating-2

An example in which carry is generated:

434 x 101 = ?

repeating-3

Let us practice more now:

a 53 × 101                           b 167 × 1001                           c 423 × 1001
d 739 × 1001                       e 4567 × 10001                       f 79 × 10101