Multiply by 99, 999, etc.

In this section, we are going to study another special method of multiplication where a number is multiplied with another number containing all digits equal to “9”, i.e. 99, 999 and so on.

Vedic Sutra:

• Ekanyunena Purvena (By One Less than the Previous One)
• Nikhilam Navatascaramam Dasatah (All from 9 and the Last from 10)

The product of the two numbers can be easily computed in two parts.

• The first part of the answer is: the number being multiplied by 9’s is first reduced by 1.
• The second part of the answer is: then “All From 9 and the Last From 10” is applied to the number being multiplied.

Let us understand this with an example:

42 x 99 = ?

 

523 x 999 = ?

Let us practice more:

a 69 × 99                            b 72 × 99                                c 26 × 99

d 35 × 99                            e 758 × 999                            f 6754 × 9999

g 77 × 999                          h 134 × 9999                         i 9889 × 99999