AnExtremelyLongName

I like your method better! It insures 100% accuracy!

(1) This is a math forum. I recommend going to brainly.

(2) We are not here to write an entire CER for you

(3) We have no idea what this question is about.

Here is hunch:

An expression like x * y keeps the number of zeroes as long as x and y do not contain (2 * 5) or any factor of ten like (25 * 4) etc.

Ex: one zero (10 * 11 = 110) four zeroes (100 * 100 = 10,000)

 - In the current problem, the numbers obviously do not have any factor of ten. So:

1,000,000,000,002 * 999,999,999,996​ we count the zeroes, getting an answer of \(\boxed{11}\)?

But you said... wait now I'm super confused and I lost my train of thought

1,000,000,000,002 * 999,999,999,996

How will we know how many zeros that has?

Good idea!

_________

So by the (a - b)² = (a + b)(a - b), can we work this further? I am struggling as much as you right now.

Oh shoot, you are right. Hmmm. Perhaps you can simplify 999,999,999,998² into multiple, smaller exponents. I can't think of anything else.

Hint:

Evaluate: \(\frac{36}{60}\)

Hello nchang! I like your name, it probably reveals your last name in real life! >:D

Know:

A number only has a 0 in it if when factored, has 2 * 5 in it.

Solve:

When you factor 999,999,999,998², count how many (2 * 5)s it has.

Hellow Qwertyzz!

Do you know what floor function is? Just a reminder: Floor(3.9) = 3

Sqrt(1) = 1

Sqrt(2) = 1.414...

Sqrt(3) = 1.732...

Sqrt(4) = 2

Sqrt(5) = 2.236...

...

Sqrt (9) = 3

....

Sqrt(16) = 4

See the pattern?

The terms evaluate into an integer and only increases at the next perfect square.

Solving:

1 + 1 + 1 + 2 + 2 + 2 + 2 + 2 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 4 + 4 + 4 + 4

 = Gonna let you do some work