help! |
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 Dec 7 2004, 11:31 PM
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#1
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 jellyfishing, jellyfishing  Group: Member Posts: 1,174 Joined: Oct 2004 Member No: 55,185  |
aaacch i don't get this math problem, i'm really stupid. it's a junior high problem, so maybe someone could help?
Claire finished her assignment early, so her teacher suggested that she find the last digit of the product 3 x 3 to third power x 3 to fifth......x 3 to nineteenth. The entire product was too big for her calculator, but she still found the last digit. What is the last digit? Explain how she determined her answer i know that if you add all the exponents, you'll get 3 to the 100th power, since 3+5+7+9+11+13+15+17+19=100 right (those are the exponent values...), so it'd be 3 to the 100th power. on my calc i got 5.153775207 to the 47th power.....what next?!?!!? sorry if this is in the wrong board...i saw someone ask for math help awhile back, so i figured it'd be OK 
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Dec 7 2004, 11:41 PM
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#2
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 Quand j'étais jeune... Group: Staff Alumni Posts: 6,826 Joined: Jan 2004 Member No: 1,272 |
QUOTE 5.153775207 to the 47th power.....what next?!?!!? I guess you could rewrite it as 5.15 x 10^47  , but that's not the answer... it's weird that you have to find the last digit. Let me check around and I'll edit if I find a better answer.
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Dec 7 2004, 11:44 PM
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#3
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 白人看不懂 !!!! Group: Member Posts: 3,838 Joined: Aug 2004 Member No: 40,824 |
do you mean to find the last digit of the product of
(3^3)(3^5)(3^7)(3^9)(3^11)(3^13)(3^15)(3^19) ?? |
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Dec 7 2004, 11:47 PM
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#4
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Quand j'étais jeune... Group: Staff Alumni Posts: 6,826 Joined: Jan 2004 Member No: 1,272 |
This page has something similar except with the number two instead. I'm reading it right now, but I think you'll find your answer there.
I can tell you now the it will end with one of these numbers: 1, 3, 9, 7... 3=3 3^2=9 3^3=27 3^4=81 3^5=243... 3^8=6561 3^12=531441 You'll notice that every 4th power give the same last digit. So powers of 4 8 12 16... should all have the same last digit. I think that I last digit should be 1 for the 100th power. Okay, never mind.. I don't know how to do it. |
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Dec 8 2004, 12:20 AM
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#5
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 :hammer: Group: Staff Alumni Posts: 9,849 Joined: Mar 2004 Member No: 7,700 |
I think the last digit is going to be 1.
Because uh.. for every even number exponent, the last digit changed from 1 to 9. 3^2 = 9 3^4 = 81 3^6 = 729 3^8 = 651 3^10 = 59049 3^12 = 531441 So I wrote all the even numbers up to 100 and basically patterned it out. Haha. BUT all the exponents divisible by 4 have a last digit of 1. And 100 is divisible by 4 so the last digit should be 1. |
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Dec 8 2004, 01:15 AM
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#6
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jellyfishing, jellyfishing Group: Member Posts: 1,174 Joined: Oct 2004 Member No: 55,185 |
oooh thanks, i get it now!
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Dec 8 2004, 01:20 AM
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#7
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 Oh you'd be surprised Group: Member Posts: 2,406 Joined: Mar 2004 Member No: 7,886 |
im sick of math problems..sorry. hahah
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Dec 8 2004, 01:41 AM
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#8
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jellyfishing, jellyfishing Group: Member Posts: 1,174 Joined: Oct 2004 Member No: 55,185 |
wait, wouldn't the pattern alternate between 3 and 7??
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Dec 8 2004, 01:43 AM
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#9
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Quand j'étais jeune... Group: Staff Alumni Posts: 6,826 Joined: Jan 2004 Member No: 1,272 |
It alternates between 1, 3, 9, 7. Just use a calculator and write out the numbers on a piece of paper. You'll see the pattern.
Every 4th power has the same ending digit, which happens to be 1. By the way, it would be 1 instead of 3 because you start with 3^1 and then 4th power ends with 1. This post has been edited by uninspiredfae: Dec 8 2004, 01:58 AM |
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Dec 8 2004, 01:53 AM
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#10
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白人看不懂 !!!! Group: Member Posts: 3,838 Joined: Aug 2004 Member No: 40,824 |
omg, you guys...i'm lost...=( why must math be so complex??
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Dec 8 2004, 02:02 AM
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#11
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jellyfishing, jellyfishing Group: Member Posts: 1,174 Joined: Oct 2004 Member No: 55,185 |
QUOTE(uninspiredfae @ Dec 7 2004, 10:43 PM) It alternates between 1, 3, 9, 7. Just use a calculator and write out the numbers on a piece of paper. You'll see the pattern. Every 4th power has the same ending digit, which happens to be 1. By the way, it would be 1 instead of 3 because you start with 3^1 and then 4th power ends with 1. ooooh i think i see what you're saying. so the 3 to the 100th power ends with a one right? but did you just write it all out or use some sort of technique?? |
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Dec 8 2004, 02:16 AM
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#12
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:hammer: Group: Staff Alumni Posts: 9,849 Joined: Mar 2004 Member No: 7,700 |
QUOTE(pAtRiCk_sTar @ Dec 7 2004, 11:02 PM) ooooh i think i see what you're saying. so the 3 to the 100th power ends with a one right? but did you just write it all out or use some sort of technique?? If the exponenent is divisble by 4, then the last digit will be 1. In this case, 100 is divisible by 4, and therefore the last digit of 3^100 is 1. |
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Dec 8 2004, 02:30 AM
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#13
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jellyfishing, jellyfishing Group: Member Posts: 1,174 Joined: Oct 2004 Member No: 55,185 |
QUOTE(x_angawhomps @ Dec 7 2004, 11:16 PM) If the exponenent is divisble by 4, then the last digit will be 1. In this case, 100 is divisible by 4, and therefore the last digit of 3^100 is 1.  yes, i finally grasped it!! thanks so much everybody 
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Dec 9 2004, 12:16 AM
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#14
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 i'm susan Group: Official Member Posts: 13,875 Joined: Feb 2004 Member No: 5,029 |
it would be so cool if we had a homework help forum. or do we have it?.......
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Dec 9 2004, 12:19 AM
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#15
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 durian Group: Staff Alumni Posts: 13,124 Joined: Feb 2004 Member No: 3,860 |
Problem solved.
 TOPIC CLOSED. |
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