How many digits does the product contain?

[Vemuri]

How many digits does the product of 4^12 and 5^23 contain?
A. 12
B. 13
C. 23
D. 24
E. 35

I do not have the OA. I hope there is a easy way to solve this problem.

[scoobydooby]

4^12 * 5^23
=(2^2)^2 * 5^23
=2^24 * 5^23
=(2*5)^23 *2
=10^23 *2

10^23 gives 23 zeroes
10^23 *2 therefore has 2+23 zeroes
=24 digits

hence, D

[Vemuri]

4^12 * 5^23
=(2^2)^2 * 5^23
=2^24 * 5^23
=(2*5)^23 *2
=10^23 *2

10^23 gives 23 zeroes
10^23 *2 therefore has 2+23 zeroes
=24 digits

hence, D

Hey soobydooby,

That's a very good solution.

[dumb.doofus]

4^12 * 5^23
=(2^2)^2 * 5^23
=2^24 * 5^23
=(2*5)^23 *2
=10^23 *2

10^23 gives 23 zeroes
10^23 *2 therefore has 2+23 zeroes
=24 digits

hence, D

Hey soobydooby,

That's a very good solution. If 10^23 has 23 zeros, multiplying this number with 2 should not change the number of zeros right? You seem to have hurried up in the last part. I think the answer should be 23 digits, i.e. C.

I think it is correct.. it should be 24.
10^5 = 100000 There are 5 zeros..

so 10^23 will have 23 zeros.. also we have 1.. so altogether 24 digits..

[g2000]

10^23 *2

I'm just curious the number of zeroes. It seems it's 23 zeroes, doesn'it?

If multiply by 2, that only changes the coefficient of 10^23.

For instance,
10^2 * 5
= 100 * 5
= 500
That's not 5000!?! (the extra mysterious one!?!)

[DeepakR]

Thanks Scoobydooby for the clear solution:

I think the answer should be 24. For eg.) 10^1 * 2= 20 2 digits and now 10^2 * 2= 200 we get 3 digits i.e the power of 10 + 1. So in case of 10^3 * 2 = 2000 we have power of 10 =3 and hence 3 + 1 = 4 digits.

Similarly for 10^23 * 2 we'll have 24 digits.

-Deepak