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.
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How many digits does the product contain?
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scoobydooby
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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
=(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
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dumb.doofus
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I think it is correct.. it should be 24.Vemuri wrote:Hey soobydooby,scoobydooby wrote: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
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.
10^5 = 100000 There are 5 zeros..
so 10^23 will have 23 zeros.. also we have 1.. so altogether 24 digits..
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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!?!)
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!?!)
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DeepakR
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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
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
