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How many digits are in the number 50^8 × 8^3 × 11^2?

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Math Expert
Joined: 02 Sep 2009
Posts: 56307
How many digits are in the number 50^8 × 8^3 × 11^2?  [#permalink]

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28 Apr 2016, 01:09
00:00

Difficulty:

65% (hard)

Question Stats:

57% (01:41) correct 43% (01:50) wrong based on 144 sessions

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How many digits are in the number 50^8 × 8^3 × 11^2?

A. 22
B. 20
C. 19
D. 18
E. 17

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Math Expert
Joined: 02 Aug 2009
Posts: 7763
Re: How many digits are in the number 50^8 × 8^3 × 11^2?  [#permalink]

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28 Apr 2016, 02:29
1
1
Bunuel wrote:
How many digits are in the number 50^8 × 8^3 × 11^2?

A. 22
B. 20
C. 19
D. 18
E. 17

As we can see 5s and 2s in the term, lets get it in terms of 10s..

$$50^8 × 8^3 × 11^2 = (5^2)^8*2^8*2^{3*3}*11^2 = 5^{16}*2^{17}*11^2 = 10^{16}*2*121$$
so 3 digits from 2*121 and 16 trailing zeroes from $$10^{16}$$..
total = 3+16 = 19
C
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Joined: 06 Nov 2014
Posts: 1877
Re: How many digits are in the number 50^8 × 8^3 × 11^2?  [#permalink]

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29 Apr 2016, 00:45
2
1
Bunuel wrote:
How many digits are in the number 50^8 × 8^3 × 11^2?

A. 22
B. 20
C. 19
D. 18
E. 17

This might look to be a difficult question on the first glance.
Whenever you are asked to find the number of digits, try to bring the number in multiples of 10. This way, we can wasily calculate the umber of 0's through the powers of 10

50^8 × 8^3 × 11^2 = (5^2*2)^8*2^9*11^2 = 5^16*2^17*11^2 = 2*11^2*10^16 = 242*10^16
Hence we would have 16 trailing 0's and the three digits from 242
Total digits = 3 + 16 = 19

Correct Option: C
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Re: How many digits are in the number 50^8 × 8^3 × 11^2?  [#permalink]

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10 May 2019, 04:46
Bunuel,

Thank you
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Re: How many digits are in the number 50^8 × 8^3 × 11^2?   [#permalink] 10 May 2019, 04:46
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