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Description:
A pattern exists among the units digits of the powers of 3, as shown below. What is the units digit of 3⁹⁵?
Transcript
- 00:01
Okay C t s baring math people Here we go
- 00:04
Another question for you Ah pattern exists among the unit's
- 00:07
digits of the powers of three is shown below right
- 00:11
down there What's the unit's digit of three to the
- 00:14
ninety fifth power And note the problem gives you that
Full Transcript
- 00:23
The unit's digit of nineteen thousand six hundred eighty three
- 00:26
is three No one wants to figure out three to
- 00:29
the ninety fifth by hand So it's calculator time Yeah
- 00:33
of course This on lee seems like a good idea
- 00:35
until we realized that the scientific calculator on ly presents
- 00:38
answers in scientific notation which doesn't help us find ah
- 00:42
units digit like this thing right here Instead we gotta
- 00:45
look for a pattern in the powers of three which
- 00:46
is a well with problems suggested in the first place
- 00:49
The digits cycle through a one three nine and then
- 00:53
seven before beginning again we see the pattern there So
- 00:56
the task now is to create a formula that tells
- 00:58
us which of these units digits applies to any given
- 01:01
number without counting to ninety five In groups of four
- 01:05
we have three to zero through the fourth and then
- 01:07
through the eighth all of those have units digits of
- 01:10
one notice that the exponents of these terms are all
- 01:13
evenly divisible by four Meanwhile we have three of the
- 01:16
first real fifth and three to the ninth and they
- 01:18
all have units digits of three Well the exponents of
- 01:22
thes terms aren't divisible by four but they all share
- 01:25
a remainder of one when divided by four So that's
- 01:29
the pattern when divided by four exponents with remainder sze
- 01:33
of to have units digits of nine while exponents with
- 01:37
reminders of three have units digits of seven All right
- 01:40
now let's give ninety five a shot Well ninety five
- 01:43
divided by four is twenty three remainder three right So
- 01:46
since the remainder is three the unit's digit is seven
- 01:51
So there we go The answer here is d It's
- 01:53
got to be seven right See have it gets it
- 01:55
gets you cleverly there in number four It's always a 00:01:58.213 --> [endTime] seven That's it That was kind of tricky
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