Question

100^25-25 is writtern in decimal notation the sum of digits is

Answer 1

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Answer: 444

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Okay. The given number is 25 subtracted from, 100 raised to the power 25, isn't it?

What about 100 raised to the power 25?

$100^{25} \\ \\ (10^2)^{25} \\ \\ 10^{2 \times 25} \\ \\ 10^{50}$

It is like 1 followed by 50 zeroes.

Like this:

100000000000000000000000000000000000000000000000000

Whoa!!!

Okay. The sum of the digits is only 1.

But what about 100²⁵ - 25?

It would be like the following:

99999999999999999999999999999999999999999999999975

Amazing!!!

Isn't it hard to find the sum of digits of the number given above, one by one?

Okay, let me do it in a curved way!

Go back to 100²⁵. We saw that it is 1 followed by 50 zeroes.

So it is a 51-digit number.

Isn't it the smallest 51-digit number? Yep!

So what about 100²⁵ - 25 ?

It's a 50-digit number.

When we subtract 25 from a 5-digit number 10000, we get a 4-digit number 9975.

Like this, we got a 50-digit number when we subtracted 25 from a 51-digit number.

But this doesn't hold true at all. It requires some conditions.

Okay. When we wrote the 50-digit number 100²⁵ - 25 in decimal notation, we found that all digits, except the last two ones, are 9 each. And tens and ones digits are 7 and 5 respectively.

Here, we get that, there are 48 nines.

So, didn't we get the answer?!

(48 × 9) + 7 + 5 = 432 + 12 = 444.

Nice answer.

Okay. I hope you may get a clear picture of my answer.

If you have any doubt, please ask it to me.

And also, don't forget to mark my answer as the brainliest if this helps you.

     

Thank you. :-))

     

#adithyasajeevan