Answer :
To determine how many 4s will be in the result of multiplying 2222222222222 by 11, we approach this step-by-step using the multiplication process.
When a number is multiplied by 11, a useful pattern emerges. Each digit in the original number contributes to two digits in the result.
Let's break it down with this specific multiplication:
Write out the number:
[tex]2222222222222[/tex]
Consider the multiplication by 11:
Using the '11 rule for multiplication', you add adjacent digits. Here's how:
Start from the rightmost (units) digit, simply add 0 to the last digit (since there is no digit to the right):
[tex]2[/tex] (the last digit)
Moving left, add each pair of adjacent digits:
[tex]2 + 2 = 4[/tex]
Continue this for all pairs:
[tex]2 + 2 = 4[/tex] again
Repeat this process for each pair in the sequence:
[tex]2 + 2 = 4[/tex], again and again, until you reach the leftmost digit.
When you reach the first digit, just add this digit as it only has one neighbor to the right:
Add it by a non-existent 0 for the initial carry:
[tex]2 + 0 = 2[/tex]; this provides the first digit of the sum.
The overall multiplication using this pattern for 2222222222222 by 11 would result in a sequence where most digits become 4s, except the very first and very last.
In summary, based on the pattern, all the sums result in 4 except on the edge of the sequence. It's a pattern where most intermediate sums are four. This sequence would repeat, meaning each two adjacent 2s produce a 4.
Therefore, there will be 11 digits of 4 in the product [tex]24444444444442[/tex].
