What is the units digit of
1 2 3 × 4 5 6 7 8 9 ?
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I grasp your solution but it's quite confusing for those who are not mathematician just make it simple for universal understanding...for universal concern they already know the unit word...why not multiply the last digit of two factor 3 and 9 and their product is 27, unit digit is 7 and there every level of knowledge could get it.
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well since you did the explanation for me, I don't need to say anything more ;]
Wow nice explanation Oliedor, now I actually understand it. I struggle with math alot, so I use brilliant to help myself. Thanks. :)
Since the units digit is not affected with any carry from previous multiplications...simple the number in units digit of the product of the last two digits of the given number will be the answer
plz make 120 using 5 zeroes
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0 Factorial=1 (0!+0!+0!+0!+0!)!, (1+1+1+1+1)!=5!=120; lets enjoy
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multiply the numbers of the telephone how much do u get?
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@Swetha Vaidyanathan – answer is 362880
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@Archana Raghavan – archana sister how to did it multiply the numbers of the telephone how much do u get?
123X456789=56185047 Last digit is 7
Just multiply 3 by 9, the answer is 27. So, the last unit will probably be 7.
What's the theorem behind this and where can I find it proved or explained?
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Basically the idea behind the units digit is that a number in base 10, when divided by 10, whatever remainder that it leaves behind will be the units digit. Hence we take the number modulo 10 to see wat the remainders are. Taking 123 modulo 10 we know the remainder is 3 when 123 is divided by 10, i.e. the units digit is 3. Similarly when 456789 is divided by 10, the remainder is 9, hence 456789 is congruent to 9 modulo 10. Multiplying these two congruences we find that the product as a remainder 27 when divided by 10, but since 10 can go in to 27 two more times, we will have that the remainder will be 7, which implies that the units digit of the product will be 7.
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Thank you for explaining! I understood the basic concept, but I really wanted to know what the reasoning behind the idea that we can multiply the two congruencies. I've been having problems with the techniques trainer, so I can't look it up there...
You are very much clear. But simple is multiplying 3 and 9.
In fact, this is the real answer in mathematic form, since it can determnie not only the unit, also maybe the 2 last digit or whatever.
simply multiply these 2 num then the unit (last num) in the becoming answer is is unit num and that is 7
7 ans kesa aya help me
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by multiplying the last digits of both the numbers i.e 123 x 456789.
superb question
I have followed the same method
Since the units digit is not affected with any carry from previous multiplications...
7
who will answer:::::::------
The lengths of two cubes are positive integers. The difference between their volumes can be found from the set {8, 7, 11, 21, 23, 15, 29, 33, 37, 39}. Find all possible lengths of the smaller cube.???
to find out the units digit of 123 x 456789 is just by multiplying 3 with 9 and then by paying attention to the units digits of 3x9....finally we got 7
good enough...thnx
What is the units digit of 123X456789=56185047 Last digit is 7
what is (mod 10)
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[mod or %] is an binary operator such that a % b will give the remainder value when a is divided by b..
yr mjhe to smjh nh arha kch smjhao kch :/
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In what language is this again?
fareeha kia smj nahi aya ??? unit digit ho hota ha jo unit place pe ho kisi bhi quantity ma ....
thats the most easy answer yaar.....multiply the first unit's place in both the nos. i.e 3 X9=27 where 7 will be the unit place whatsoever the other number be....simple
The units digit of 123 × 456789 is equal the units digit of 3 * 9 <=> the result is 7
Yeah,I got it
not understand~please explain
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"What's the problem with you?" Tell me what you don't understand?
If we want to find the unit of any long or short number multiplied by any number, we could find it by multiplying the last digit with last digit, then from the answer the unit of the answer will be the correct answer. Eg: 3*9=27 so the unit of it will be the unit of total. Answer is 7.
multiply only unit digit place values 9*3=27 and unit'splace value ans will be 7
right. It is the easyest way.
First of all you multiply 123*456789 then the becoming ans will be 56185047 ... then u know hat the extreme last number is a unit ... THEN the unit in this answer is (7).
123*456789=56185047 so unit digit is 7
But more easy is to only multiply 3 and 9.
:P
Yup 9*3 why waste unecessary time to find out the unasked..:P
I have followed it
what is unit digits??
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Thank you to fell free to question. The units digit is the rightmost digit of the number. For example for the number 327, 7 is the units digit and means 7 units i.e. 7 ones, giving a total of 7 2 is the tens digit and means 2 tens, giving a total of 20 3 is the hundreds digit and means 3 hundreds, giving a total of 300
123*456789= 56185047 so as you can see 7 is in the units so 7 is the answer
There is no need to do the whole multiplication problem. Just multiply the units digit of 456789 by the units digit 123. 9x3= 27, and the units digit of 27 is 7. Therefore 7 is the answer.
you need not multiply the complete number.instead multiply the last digits 3 x 9 = 2(7) so 7 is the correct answer
the units digit is the rightmost digit of the number. For example for the number 327, 7 is the units digit and means 7 units i.e. 7 ones, giving a total of 7 2 is the tens digit and means 2 tens, giving a total of 20 3 is the hundreds digit and means 3 hundreds, giving a total of 300
so if the rightmost (i.e. units) digit of a number is even, then the number is divisible by 2
3*9=27... only 7 remains the units digit
Multiply the unit digits of both number which are 3 and 9 , we got 27 in which 7 is unit digit.. So answer is 7
Multiply 3 and 9 , the last digits of the two numbers and you'll get 27 whose unit digit is 7
The last digit of any number is called unit.When we multiply 123 x 456789 = 56185047, so the last digit 7.
When you multiply two numbers, the last digit of the product is the last digit of the product of the two numbers. So the last digit of 123 x 456789 comes from the last digit of the product of 3 and 9 which is 7.
Just take the unit digit of each number ,multiply the one-digit numbers and take the last digit of the product of the multiplication.In this case 1 2 3 ∗ 4 5 6 7 8 9 . 3 ∗ 9 = 2 7
3 * 9 = 27 hence 7 is the units digit.
multiply 123 by 456789 then the result will be 56185047. unit digit is also known as ones digit. in the result, 7 is the ones digit.
By multiplying the last digit (3 and 9) get 27. So, the number of units of the product is 27.
123x456789=56185047 and the unit place is 7
units digit is nothing but the last digit so on multiplying the last digits of the two numbers i.e., 3 & 9 by multiplying these 2 numbers we get 27 and the last digit of this number is 7
multiply the units digit of both the no.s..its 27..unit digit in 27 is 7.so the ans is 7
unit digit of multiple*unit digit of multiplier=7
we can just multyply unit digits ie 3 * 9=27 and the unit digit of 27 is 7 will be the unit digit of the 123*456789
just multiply unit digits of both values
It's simply as same as the units digit of 9x3 = 27.. so, the units digit is 7..
Multiply the last digit(Unit digit) of two numbers(123 & 456789) and take the unit digit from the result Step1: last digit of 123 is 3 and last digit of 456789 is 9 Step2: 3*9=27 Step3: Unit digit(last digit) of 27 is 7 Answer is 7
3*9=27 and 7 is unit digit.
All you need to do is, multiply both units digit to get the answer. i.e. 3*9 =27. Now, 7 will be the units digit while 2 will be carried over!
simply mulitiply the 2 no. and done its only 2nd unit and see the result
123 x 456789=56,185,047......7 is in the units place
123x456789=? there is no need to multiply all the digits. as we know that we have to find only units digits, by multiplying only units digits we can find unit digit of above problem. It's quite easy.
multiply the last digits and write the units digit of the product. 123 456789. multiply 3 and 9. 9 3=27. 7 is the units digit of the product .so 7 is the units digit of 123*456789
A digit in a number has two weights, one face value and the other power value. The power value in a number system is a power of the base. In decimal category the power value is a power of 10 beginning from the least whole number. The unit place has the power value 1 . In order to find the number in the unit place of the product you have to multiply the corresponding elements in the numbers to be multiplied and get the unit digit value.. So in our example we get 27(3x9) and the unit place in 27 is 7.. too simple but confusing for a beginner. .
basic multiplication......multiply the units digit of the 2 given numbers and take the units digit of the product that is your answer
the easiest way to multiply any number is......for example.. (45x24).... just multiply the first two digits to the the first digit of the answer that is the first digit of 45x24 is 8 and now multiply the across numbers and add them up..... that is 4x4 +5x2=26 .... so now if the answer u get is of a single digit than directly write the number besides the first digit of the answer ....if it is a double digit number tha add the first digit of it to first digit of the answer and next to write the number which is left and than at last multiply the last two digits of the number and proceed as the above ..(that is 5x4=20) than add it to the answer tha this is how u get it ..... the solution of (45x24=1080)...... that is add the first digit of 26 to 8 which is 10 and write the letter besides 10 which is nothing but 6 in the given problem that is 106 now add the first digit of 20 to the number 6 which is 6+2=8 and write the remaining number besides it which is 0 which equals to 80 now combine the complete number that is 1080 .... which is the answer of (45x24)..... friends the procedure which i hav texted is very long but dont think that the method is very long ......actually it is very short and easy ..and we get accurate answers with it and u can multiply any number with any other number by this method very easily
The unit digits of the two factors are 3 and 9 thus give an answer of 27 and 7 is the unit digit.
For finding the units digit,the number in the units digit of the numbers to be multiplied will only make a difference..Therefore 9 x 3 =27 and hence unit digit is 7.
simply multiply the unit's digits of the two given numbrs.
just multiply unit digit of both the numbers ie. 3*9=27 here the unit digit is 7 hence correct ans. is 7
Multiply 3 x 9 and remove all the digits except for the ones digit. The ones digit is your answer.
just multiply it and the rightmost digit is the units digit
multilply unit digits of both numbers
the unit digit of a multiplication is just unit digit of multiplication of unit digit of multiplying numbers. So unit digit in multiplication of 3 and 9 is 7.
Multiply unit digit of both numbers and in the answer neglect tens digit.
It is very simple! The units digit of this statement is going to be the last digit of the products of 3 and 9.
just multiply the units digit i.e.,3 and 9
Simply take the product of the ones digits.
3 ∗ 9 = 2 7
Since their product is a two-digit number, simply take the ones digit.
The answer is 7 .
3*7=27 then last digit is 7 and bingo that's the answer!
just multiply the units digit from both numbers and take the units digit of the result
the last two numbers are 3 and 9 therefore 3*9 = 27 so unit digit is 7
product of unit places of both numbers 3*9 =27 ,hence 7 is the unit digit.
Just take the last digit of both numbers and multiply them.From the resulting product take the last digit which is the answer.In the above problem take 3,9 and multiply them 3x9=27.the last digit 7 is the answer
take lst digit of bith no. i,e. 3 and 9 then multiply them 3*9=27 then take last digit 7
You are correct
9*3=27 so, 7 comes in the units digit
123 x 456789 has 3 as units digit of 123 and 9 as unit digit of 456789 ,..if they are calculated they will have unit digit = 3 x 9 = 27 ,..which the units digit is 7
3*9=27 so last digit will be 7
multiply the unit digits of two no's ,the unit place of resultant one is the unit place of whole multiple.
To find the unit digit of any multiplication take the unit digits of the numbers. In this case 123 x 456789, Take 3 and 9, multiplication of 3 and 9 is 27 and the unit digit will be 7
We can know units digit when we multiply unit digits of the given numbers. So 9x3 = 27 In 27, 7 is the unit digit. Hence answer is 7. Note: Do not follow same method in finding ten's or hundred's etc.. digit of a number
The unit digit of the product of multiplicands is the unit digit of the product of the unit digits of the multiplicands. Therefore, the unit digit of (9 x 3) i.e. 27 is 7. So, the unit digit of (123 x 456789) is 7.
Multiply unit digits of both numbers and retain the unit digit of resultant.
3*9=27 THEREFORE UNTIS DIGIT WILL BE 7
multiplication of unit places will give you 27. so that last digit will come as 7
The units digit of any product will be the units digit of the units digit of the first number times the units digit of the second number. In other words, you multiply the numbers in the one's place of both numbers and the number in the one's place of the result is what you're looking for.
As we know, to know the units digit of a multiplication, we need to only multiply the last digits of the given numbers. So 3*9 = 27, and thus the Units digit comes out to be 7
Only the last digit of the product of the units place of both the numbers , others are 0. 3*9=27 , take 7 which is your answer.
3 * 9 = 27, units place is 7 so the ans is 7
when u multiply the unit digit of both the numbers that is 3 and 9 you get 27 and 7 is the unit digit of 27 and hence is the answer ...............
Since We need to find unit digit of solution, we just have to consider the unit digit of 3*9 and it is 7.
Just multiply the last two digits of the number. The last digit of the product is the answer
When any 2 nos. are multiplied, to find the units digit of the product, we can simply multiply the units digit of the two nos. which are multiplied in the question. The units digit of the product of that will be the units digit of the actual product in the question. Here, the given nos. are 1 2 3 and 4 5 6 7 8 9 which have units digit 3 and 9 respectively.
So, product of the units digit = 3 × 9 = 2 7
The units digit of 27 is 7, so we get the units digit of the product in the question as 7 .
the units digit is the rightmost digit of the number.so 3 and 9 are two unit digit n since 3*9=27 n 7 is the units digit of 27 so answer is 7
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Yes, that's the trick to find units digit for any product of 2 nos.
consider only unit digit 3 × 9 = 27 the unit digit of 27 is 7
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1 2 3 ≡ 3 ( m o d 1 0 ) ,
4 5 6 7 8 9 ≡ 9 ( m o d 1 0 ) ,
∴ 1 2 3 × 4 5 6 7 8 9 ≡ 2 7 ≡ 7 ( m o d 1 0 ) .