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Math Help - Maths Word Problem Homework

  1. #1
    bob
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    Maths Word Problem Homework

    I'm stuck on this maths word problem for homework.. please help.

    The first 100 positive whole numbers are multiplied together to form the number N.
    (a) What is the very last right-hand (ie "units") digit of N? Explain your answer.
    (b) What digit is in the 19th place from the right? Explain your answer.

    Thank you.
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    Quote Originally Posted by bob View Post
    I'm stuck on this maths word problem for homework.. please help.

    The first 100 positive whole numbers are multiplied together to form the number N.
    (a) What is the very last right-hand (ie "units") digit of N? Explain your answer.
    (b) What digit is in the 19th place from the right? Explain your answer.

    Thank you.
    The last digit has to be 0.
    Since any whole number multiplied by, say, 10, equals zero.

    And I think... the 19th may also be...
    10,20,30,40,50,60,70,80,90,100 add in a zero, as do 5*2,12*15,22*25,32*35,42*45,52*55,62*65, 72*75, 82*85, & 92*95.

    Aye, there's 20 of them. So the 19th place from the right is also a 0.
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  3. #3
    bob
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    Hi Unenlightened, that was quick thank you very much you are a life saver.

    Bob
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    Notice that N=100!.
    100! has a factor of 5^{24}.
    So N has 24 'trailing' zeros. (Ends in 24 zeros.)
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  5. #5
    bob
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    Hi Plato

    Thanks for replying.

    Please would you explain how N=100. I was trying to multiply all the numbers together to get N.
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  6. #6
    Air
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    Quote Originally Posted by bob View Post
    I'm stuck on this maths word problem for homework.. please help.

    The first 100 positive whole numbers are multiplied together to form the number N.
    (a) What is the very last right-hand (ie "units") digit of N? Explain your answer.
    (b) What digit is in the 19th place from the right? Explain your answer.

    Thank you.
    Multiplying the first 100 numbers means that you are doing the factorial of 100. 100! = 100 \times 99 \time 98 \times ... \times 1.

    (a) Lets say you did 99 \time 98 \times ... \times 1 and last step was to multiply be 100 to get 100!. If you multiply any number by 100, what is the last digit?

    (b) Try to understand how many zeros that 100! has then you many be able to work out what the 19th value is.

    Spoiler:
    This website talks about 100!, giving it's value and explaining how many zero's it has.

    The answer to the question about 100! (100 factorial)
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    Quote Originally Posted by bob View Post
    Please would you explain how N=100. I was trying to multiply all the numbers together to get N.
    You don't understand. That is 100!, one hundred factorial.
    Like 5!=(5)(4)(3)(2)(1)=120.
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  8. #8
    bob
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    Hi Air and Plato

    Thanks for explaining.

    I've just started factors at school, it is taking me a little while to understand the topic properly.
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