Okay, lets see if I can clear it up. There are 100 sevens multiplied together and the problem wants to know what is the ones digit. For example here is the product of five twos (5)(5)(5)(5)(5) and the ones digit of the product is a 5. This problem says there are one hundred sevens...(7)(7)(7)(7)(7)... so what is the ones digit of the product. Not 100 x 7.
Dani I disagree because 7x7 is 49 and 49+49=108...or something and thats not what the question wants to know... 49x7 is 343 and thats only 3 of the 100 we need to multiply we only need to do 4 7s in a row if we wanted the answer to be 700! well it equals more!!!
Leslie, you are on the right track. 7 x 7 = 49 7 x 7 x 7 = 343 7 x 7 x 7x 7 = ---1 7 x 7 x 7 x 7 x 7 = - - - - -7 7 x 7 x 7 x 7 x 7 = ------9 . . . So...look everyone! What do you notice?
I agree with sloan, kinda, but the question doesn't want to know what 10 to the 100th power is, it wantes to know 7 to the 100th power and although 10 alternates 1,9,1,9, 7 alternates 9,3,1,7,9,3,1,7!
Ya, I agree with Leslie. The ones place goes 9,3,1,7. OK so that is 4 numbers so you do 100 divided be 4 which is 25. So you need to go through the patteren 25 times to get the right number. Which is a 9. So the ones digit is going to be a 9! Right?
The correct pattern is 1, 7, 9, 3. 7 to the 0th power is 1. 7 to the 1st power would have the ones digit equalling to 7. 7 to the 2nd power's last digit is 9. 7 to the third power's last digit is 3. Like 7 to the 0th power, 7 to the 4th power has the ones/last digit being 1.
Since, we are trying to find 7 to the 100th power, we have to divide 100 by 4 because the pattern has 4 numbers. 100/4 is 25. 25 is the amount of times the pattern repeats. The remainder is 0, which defines what the last digit of 7 to the 100th power will be. 7 to the 4th power is 1, same as 7 to the 0th power. So, the answer is 1. 7 to the 100th power's last digit is 1.
no. iris if you go through the problem correctly, you will see that the pattern is 9,3,1,7. Because the first thing is 7 multiplied by seven is 49. Then 7 times 7 times seven is 343. Then (7)(7)(7)(7)= 2401 (7)(7)(7)(7)(7)=18607. The pattern goes 9,3,1,7 So, then you do 100 divided by 4 which is 25. And then you go through the pattern (9,3,1,7) until you get to the 25 number which is 9.
Also Sloan. If you are going by every 10, it goes 9,1,9,1,9,1, etc. not 1,9,1,9,1,9, etc. but your method was right. However if you use your way or my way you still get 9, not 1.
Daniel, we are dividing 100/4 because 4 is the amount of members in that pattern. If there was a remainder, that remainder would show how many more numbers should show up in this pattern of 7 to the 100th power. And the answer has to be 1 because 7 to the 4th power is has the last digit being 1.
Iris, yes you are right about dividing by four, bur you got the pattern wrong. If you look at the problem again you will see that the pattern is clearly 9,3,1,7. And Ethan how can the answer be 7? 4 goes into 100 25 times. So if you go through the pattern you will get the answer. (9,3,1,7,9,3,1,7,9,3,1,7,9,3,1,7,9,3,1,7,9,3,1,7,9) Nine/9 is the 25th number. 9 has to be the answer.
In the first power of 7, the ones digit is 7 In the next power of 7, 7x7=49, the ones digit is 9. In the next 7x7x7, the ones digit is 3 In the next 7x7x7x7x, the ones digit is 1 The next, 7x7x7x7x7, the ones digit is 7. So the ones digits are... 7,9,3,1,...
Daniel, since you think the pattern is 7, 9,3,1 the 25th number wouldn't be 7, it would be 1. 4 goes into 100 evenly=25 times with no remainder. If there was a remainder of 1, the answer would be 7 because the pattern would go back to the start. The 25 shows how many times the pattern happens (4 numbers). We are trying to find the 25 number, which is the same as the 4th because 100/4 is equal to 25. But, since, there is no remainder or a remainder of 0, the answer is 1, or the last number of the pattern.
Yes to all of you that got 1. The pattern is 7,9,3,1. So if you consider that these four numbers are the ones digits, then it will repeat 25 times until you get to one hundred sevens. So...the 100th will end with a one.
36 comments:
The one's digit of the product is 0 because 100 x 7 = 700.
i don't really understand the question.
Okay, lets see if I can clear it up. There are 100 sevens multiplied together and the problem wants to know what is the ones digit. For example here is the product of five twos (5)(5)(5)(5)(5) and the ones digit of the product is a 5.
This problem says there are one hundred sevens...(7)(7)(7)(7)(7)...
so what is the ones digit of the product.
Not 100 x 7.
Hope that helps!
Dani I disagree because 7x7 is 49 and 49+49=108...or something and thats not what the question wants to know... 49x7 is 343 and thats only 3 of the 100 we need to multiply we only need to do 4 7s in a row if we wanted the answer to be 700! well it equals more!!!
I see that the ones diget keeps repeating, 9,3,1,7,9,3,1,7! so i think if number 1 is 7x7, not just 7 the answer is 3!
Leslie, you are on the right track.
7 x 7 = 49
7 x 7 x 7 = 343
7 x 7 x 7x 7 = ---1
7 x 7 x 7 x 7 x 7 = - - - - -7
7 x 7 x 7 x 7 x 7 = ------9
.
.
.
So...look everyone! What do you notice?
it is 7 to the 100th power not 7 times 100
every other multiple of ten it goes 1,9,1,9,1,9, like 10-9 20-1 30-9 and so on so i think the answer is 1
also... have u graded the tests yet??
I agree with sloan, kinda, but the question doesn't want to know what 10 to the 100th power is, it wantes to know 7 to the 100th power and although 10 alternates 1,9,1,9, 7 alternates 9,3,1,7,9,3,1,7!
yes im saying that 7 alternates 9317 and so on.. but every 10 sevens alternate 1,9,1,9,1,9, get it?? so the answer is def 1
So really it's 7 to the 100th power. A big 7 and a little 100.
Ya, I agree with Leslie. The ones place goes 9,3,1,7. OK so that is 4 numbers so you do 100 divided be 4 which is 25. So you need to go through the patteren 25 times to get the right number. Which is a 9. So the ones digit is going to be a 9! Right?
yes, i know that
thats what i said before but,.. i cant explain it by typing i still think the answer is 1 tho
I acctualy agree with Daniel now!
The correct pattern is 1, 7, 9, 3.
7 to the 0th power is 1. 7 to the 1st power would have the ones digit equalling to 7. 7 to the 2nd power's last digit is 9. 7 to the third power's last digit is 3. Like 7 to the 0th power, 7 to the 4th power has the ones/last digit being 1.
The pattern has 4 numbers.
Since, we are trying to find 7 to the 100th power, we have to divide 100 by 4 because the pattern has 4 numbers. 100/4 is 25. 25 is the amount of times the pattern repeats. The remainder is 0, which defines what the last digit of 7 to the 100th power will be. 7 to the 4th power is 1, same as 7 to the 0th power. So, the answer is 1. 7 to the 100th power's last digit is 1.
no. iris if you go through the problem correctly, you will see that the pattern is 9,3,1,7. Because the first thing is 7 multiplied by seven is 49. Then 7 times 7 times seven is 343. Then (7)(7)(7)(7)= 2401 (7)(7)(7)(7)(7)=18607. The pattern goes 9,3,1,7 So, then you do 100 divided by 4 which is 25. And then you go through the pattern (9,3,1,7) until you get to the 25 number which is 9.
I agree with Daniel i went through 7(7)=49 etc. and i saw the pattern
Also Sloan. If you are going by every 10, it goes 9,1,9,1,9,1, etc. not 1,9,1,9,1,9, etc. but your method was right. However if you use your way or my way you still get 9, not 1.
Daniel, we are dividing 100/4 because 4 is the amount of members in that pattern. If there was a remainder, that remainder would show how many more numbers should show up in this pattern of 7 to the 100th power. And the answer has to be 1 because 7 to the 4th power is has the last digit being 1.
With whichever number you start the pattern, the answer has to be 1.
the answer is 7 because the pattern for the first 4 numbers is 9,3,1,7. if you repeat that up to 100 you should get 7
I LIKE the way y'all are all commenting... You really do seem that you ARE helping each other. (and solving the problem) :)
Iris, yes you are right about dividing by four, bur you got the pattern wrong. If you look at the problem again you will see that the pattern is clearly 9,3,1,7. And Ethan how can the answer be 7? 4 goes into 100 25 times. So if you go through the pattern you will get the answer. (9,3,1,7,9,3,1,7,9,3,1,7,9,3,1,7,9,3,1,7,9,3,1,7,9) Nine/9 is the 25th number. 9 has to be the answer.
Daniel, Ethan, Camelia, Leslie-
In the first power of 7, the ones digit is 7
In the next power of 7, 7x7=49, the ones digit is 9.
In the next 7x7x7, the ones digit is 3
In the next 7x7x7x7x, the ones digit is 1
The next, 7x7x7x7x7, the ones digit is 7.
So the ones digits are...
7,9,3,1,...
Noah,
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so, is this 7 to the 100th power?
So the answer is 7?
you do the same thing exept do the pattern 7,9,3,1. So if you go through the pattern 25 times with that pattern the answer would be 7.
yacova, yes its 7 to the 100th power (7)(7)(7)(7) etc.
iris i see the way you went, but i still don't understand how it can be one, doesn't it have to be 7?
Daniel, since you think the pattern is 7, 9,3,1 the 25th number wouldn't be 7, it would be 1. 4 goes into 100 evenly=25 times with no remainder. If there was a remainder of 1, the answer would be 7 because the pattern would go back to the start. The 25 shows how many times the pattern happens (4 numbers). We are trying to find the 25 number, which is the same as the 4th because 100/4 is equal to 25. But, since, there is no remainder or a remainder of 0, the answer is 1, or the last number of the pattern.
Yes to all of you that got 1.
The pattern is 7,9,3,1. So if you consider that these four numbers are the ones digits, then it will repeat 25 times until you get to one hundred sevens. So...the 100th will end with a one.
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