9887341094234585×9999999999999999
Solve it in 30 seconds?
In this section, we will explore a special multiplication technique used when a number is multiplied by another number composed entirely of the digit "9", such as 99, 999, and so on.
"By One Less than the Previous One", "All from 9 and the Last from 10" using these two Vedic Sutras, we can easily compute the product of such numbers in two parts:
First part: Subtract 1 from the number being multiplied by the "9"s.
Second part: Apply the "All from 9 and the Last from 10" technique to the number being multiplied.
Let’s understand this method with an example:
92 × 99 = ?
Step 1: First part (By One Less than the Previous one): Subtract 1 from 92:
92 - 1 = 91 (first part).
Step 2: Second part (All from 9 and the last from 10): Subtract 92 from 100:
100 - 92 = 08 (second part).
Combine the two parts: 91 / 08 = 9108.
So the result is: 9108.
327 × 999 = ?
Step 1: First part (By One Less than the Previous one): Subtract 1 from 327:
327 - 1 = 326 (first part).
Step 2: Second part (All from 9 and the last from 10): Subtract 327 from 1000:
1000 - 327 = 673 (second part).
Combine the two parts: 326 / 673 = 326673.
So the result is: 326673.
5678 × 9999 = ?
Step 1: First part (By One Less than the Previous one): Subtract 1 from 5678:
5678 - 1 = 5677 (first part).
Step 2: Second part (All from 9 and the last from 10): Subtract 5678 from 10000:
10000 - 5678 = 4322 (second part).
Combine the two parts: 5677 / 4322 = 56774322.
So the result is: 56774322.
457 × 999 = ?
Step 1: First part (By One Less than the Previous one): Subtract 1 from 457:
457 - 1 = 456 (first part).
Step 2: Second part (All from 9 and the last from 10): Subtract 457 from 1000:
1000 - 457 = 543 (second part).
Combine the two parts: 456 / 543 = 456543.
So the result is: 456543.
9887341094234585 × 9999999999999999 = ?
Step 1: First part (By One Less than the Previous one): Subtract 1 from 9887341094234585:
9887341094234585 - 1 = 9887341094234584 (first part).
Step 2: Second part (All from 9 and the last from 10): Subtract 9887341094234585 from 10000000000000000:
10000000000000000 - 9887341094234585 = 1132658905765415 (second part).
Combine the two parts: 9887341094234584 / 1132658905765415 = 98873410942345841132658905765415.
So the result is: 98873410942345841132658905765415.
