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Operations & Algebraic Thinking Videos 5 videos

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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

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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