Question

If the product 1,001,001,001 x 999 × 1,000,000,000,001 is computed, how many 9's

are in the product?

Answer 1

To find the number of 9's in the product of 1,001,001,001 x 999 x 1,000,000,000,001, we need to first calculate the product.

1,001,001,001 x 999 x 1,000,000,000,001 can be written as:

(1,000 + 1) x (999) x (1,000,000,000,000 + 1)

Expanding this expression using the distributive property:

1,000 x 999 x 1,000,000,000,000 + 1 x 999 x 1,000,000,000,000 + 1,000 x 999 x 1 + 1 x 999 x 1

Simplifying each term:

999,000,000,000,000 + 999,000,000,001 + 999,001

Adding the terms:

999,000,999,001

Now we can count the number of 9's in this product. There are 3 nines in 999,001, and 9 nines in 999,000,999,000. Therefore, the product 1,001,001,001 x 999 x 1,000,000,000,001 has a total of 12 nines.