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Comment on Units Digit of 53 to Power of 35
Please I don't understand how
This article might help:
This article might help: https://www.greenlighttestprep.com/articles/units-digits-big-powers
Just use a calculator... It
That's a good idea, but it
That's a good idea, but it won't work. First of all, the onscreen calculator is very basic, and does not have an exponent button. This means you must enter 53 x 53 x 53 x 53 x 53 x 53 x 53 x .... (35 times). If you miscount, your answer will be incorrect.
So that's one problem. An even bigger problem with using the onscreen calculator is that it cannot display more than 8 digits. If a number has more than 8 digits, the calculator displays an error message. This is a problem because 53^35 is a 61-digit number.
For more information about the GRE's onscreen calculator watch this video: https://www.greenlighttestprep.com/module/general-gre-info-and-strategie...
I meant use the calculator to
Ah, sorry for the
Ah, sorry for the misunderstanding. Yes, you can certainly use the calculator to find the pattern.
The easiest approaach will be
That is, indeed, the approach
That is, indeed, the approach.
Cheers,
Brent
What do you guys mean 35/4= 8
Here's my video introduction
Here's my video introduction to remainders: https://www.greenlighttestprep.com/module/gre-integer-properties/video/840
It's true to say that 35/4 = 8.75.
So, for example, if 4 people were to share in the cost of a $35 gift, then the amount each person pays = $8.75
Of course, this works with money, since we can easily divide one dollar into smaller amounts.
However, what if we were to evenly distribute 35 puppies among 4 children?
In this case, we can't say that each child gets 8.75 puppies (at least I hope not!!!).
In this case, we could give each child 7 puppies, and have 3 puppies remaining.
Cheers,
Brent
If I have 19 to the power of
it has a cycle of 2, so 42/2= 21 so the unit digit will be 1, the last digit of the result?
if it will be the case of 2 to the power of 43
it has a cycle of 4, 43/4= 10.75 so the remainder will be the unit number = 3.
3 to the power of 44
it has a cycle of 4, 44/4=11 so the unit number is 1.
but in the case of 52 to the power of 12 with a cycle of 4, 12/4=3... and the unit number is 6, so this approach in which cases may apply?
Thank you
Sorry, but that approach won
Sorry, but that approach won't work for most/many cases.
Let's find the units digit of 19^42 first.
19^1 = --9
19^2 = --1
19^3 = --9
19^4 = --1
19^5 = --9
19^6 = --1
This has cycle 2, so when the exponent is a multiple of 2, the units digit is 1.
Since 42 is a multiple of 2, the units digit of 19^42 is 1
-----------------------------------------
Let's find the units digit of 2^43 next.
2^1 = ---2
2^2 = ---4
2^3 = ---8
2^4 = ---6
2^5 = ---2
2^6 = ---4
2^7 = ---8
2^8 = ---6
2^9 = ---2
This has cycle 4, so when the exponent is a multiple of 4, the units digit is 6.
Since 40 is a multiple of 4, the units digit of 2^40 is 6
Now let's continue the 6-2-4-8-6-2-4-8 pattern
The units digit of 2^41 is 2
The units digit of 2^42 is 4
The units digit of 2^43 is 8
---------------------------------------------
Let's find the units digit of 3^44 next.
3^1 = ---3
3^2 = ---9
3^3 = ---7
3^4 = ---1
3^5 = ---3
3^6 = ---9
3^7 = ---7
3^8 = ---1
3^9 = ---3
This has cycle 4, so when the exponent is a multiple of 4, the units digit is 1.
Since 44 is a multiple of 4, the units digit of 3^44 is 1
------------------------------------------
Here's an article with extra practice at the end: https://www.greenlighttestprep.com/articles/units-digits-big-powers
Cheers,
Brent
Dear hi
What is the unit digit of 2^96
Let's start by listing some
Let's start by listing some powers of 2:
2^1 = ---2
2^2 = ---4
2^3 = ---8
2^4 = ---6
2^5 = ---2
2^6 = ---4
2^7 = ---8
2^8 = ---6
2^9 = ---2
...etc
Notice that the cycle = 4
Also notice that, when the exponent is a multiple of 4, the units digit is 6.
Some examples: 2^4 = --6, 2^8 = --6, 2^12 = --6, 2^16 = --6, etc
Since 96 is a multiple of 4, we know that 2^96 = --6
So, the units digit is 6
Cheers,
Brent
Did I get my previous ( 53^35
thanks
Yes, I saw your comment at
Yes, I saw your comment at https://www.greenlighttestprep.com/module/gre-powers-and-roots/video/1034
However, 53 has cycle 4 (not 5), as I showed in that post.
I'm just not sure what you mean by estimation. We certainly don't want to estimate the value of 53^35
We need to make some key observations:
1) 53 has a cycle of 4 (that is it repeats itself every four powers)
2) The unit's digit of 53^n is 1 whenever n is a multiple of 4 (4 being the cycle of powers of 53)
For example, the unit's digit of 53^4 is 1, the unit's digit of 53^8 is 1, the unit's digit of 53^12 is 1, the unit's digit of 53^16 is 1, etc
Since 32 is a multiple of 4, we know that the unit's digit of 53^32 is 1
Continuing our pattern we get:
The unit's digit of 53^33 is 3
The unit's digit of 53^34 is 9
The unit's digit of 53^35 is 7
Does that help?
Hi, I tried this way- 53, i
3^1= 3
3^2= 9
3^3= _7
3^4= _1
so the continuity is 3,9,7,1
The unit digit of the exponent is 5, so 3^5= _3
so, is 3 not the answer? I referred few methods, many taught this manner. Please help.
Thanks :)
When it comes to questions
When it comes to questions involving the units digit of large powers, it's perfectly fine to ignore the tens digit of the BASE, but when it comes to the EXPONENT, you must use the entire number (i.e., you can't ignore the tens digit in the EXPONENT).
To see why, let's continue listing the unit's digit of successive powers:
3^1 = 3
3^2 = 9
3^3 = _7
3^4 = _1
3^5 = _3
3^6 = _9
3^7 = _7
3^8 = _1
3^9 = _3
3^10 = _9
3^11 = _7
3^12 = _1
3^13 = _3
Notice that:
The units digit of 3^1 is 3, but the units digit of 3^11 is 7
The units digit of 3^2 is 9, but the units digit of 3^12 is 1
The units digit of 3^3 is 7, but the units digit of 3^13 is 3
As you can see, when we ignore the tens digit of the exponent, the units digit of the power is different from when we use the tens digit of the exponent.
For the same reason, the units digit of 3^35 is different from the units digit of 3^5