Question 552422: if a number ends in zeros the zeros are called terminal zeros. For example, 520,000 has four terminal, but 502,000 has just three terminal zeros. Let N equal the product of all natural numbers from 1 through 20: 1x2x3x4 ... x20. How many terminal zeros will N have when written in standard form?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! if a number ends in zeros the zeros are called terminal zeros. For example, 520,000 has four terminal, but 502,000 has just three terminal zeros. Let N equal the product of all natural numbers from 1 through 20: 1x2x3x4 ... x20. How many terminal zeros will N have when written in standard form?
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Find ALL of the prime 5 and 2 factors.
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2 = 2*1
4 = 2^2
5 = 5*1
6 = 2*3
7
8 = 2^3
9
10 = 2*5
11
12 = 2^2*3
13
14 = 2*7
15 = 3*5
16 = 2^4
17
18 = 2*3^2
19
20 = 2^2*5
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count the 5's: 4
count the 2's: 18
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# of "10" factors: 4
# of training zeros: 4
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Cheers,
Stan H.
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