Tricky Math Problem

[CDMM1991]

I had a math workbook full of problems and this one is giving me some trouble:

How many zeroes are at the end of this number?

50 (to the power of) 20 x 20 (to the power of) 50

I got 90.

What do you guys think?

 

[RealtorGal]

Paging Mathman... Dr. Mathman, your services are requred on this thread.

 

[BittyBug]

I had a math workbook full of problems and this one is giving me some trouble:

How many zeroes are at the end of this number?

50 (to the power of) 20 x 20 (to the power of) 50

I got 90.

What do you guys think?

I always factor things to make it easier in my mind. 50^20 x 20^50 is the same as (5 x 10)^20 x (2 x 10)^50, which is the same as (5^20 x 10^20) x (2^50 x 10^50), which is the same as 5^20 x 2^50 x 10^70. Now you can express 2^50 as 2^20 x 2^30, so you get 5^20 x 2^20 x 2^30 x 10^70, or (5 x 2)^20 x 2^30 x 10^70, which is 10^20 x 2^30 x 10^70 = 2^30 x 10^90. So your answer lies in how many zeroes 2^30 has, and since the answer is none, all the zeroes are coming from 10^90, so 90 zeroes = you are correct.

 

[nicole_l]

2^30 has one zero. (Thank you TI-83+!).

 

[BittyBug]

2^30 has one zero. (Thank you TI-83+!).

But the question was about the # of zeroes at the end of the number - in other words, factors of 10. 2^30 has no trailing zeros because it's not divisible by 10. (Don't you hate word problems? They always screw you with the fine print.)