Question

Which number is irrational.

A. 0.14 sorry for not knowing math terms and such but there's a bar above the "14"

B. 1/3

C. pi 4

D. pi 6

Answer 1

@mathmate

Answer 2

Do you know what is an irrational number?

Answer 3

Isn't it a number that can be put in decimal form or percentage form?

Answer 4

can't*

Answer 5

Oops

Answer 6

In mathematics, many of the questions can be answered correctly if we know the definition of the terms. If we do not know what the terms mean, the question will appear difficult.
So the first step is to understand the meaning of the terms.

From wiki:
"a rational number is any number that can be expressed as the quotient or fraction p/q of two integers, p and q, with the denominator q not equal to zero."
" an irrational number is any real number that cannot be expressed as a ratio of integers. Irrational numbers cannot be represented as terminating or repeating decimals."

Answer 7

Are the terms clear to you now?

Answer 8

Somewhat

Answer 9

For example:
(not the same as the first option)
0.14 = 14/100 =7/50, so it can be expressed as a fraction. is it rational?

Answer 10

Yes

Answer 11

Right?

Answer 12

Good!

Answer 13

Okay

Answer 14

So a number that can become a Fraction or a decimal correct?

Answer 15

Now the number 0.13333333333...
is called a repeting decimal. It can be converted to a fraction as 2/15

Answer 16

All repeting decimals can be converted to a fraction.

Answer 17

Oooookay

Answer 18

So we're looking for a number that can't be turned into a fraction right?

Answer 19

Right!
If you need further help, let me know.

Answer 20

Oops

Answer 21

Option C and D were supposed to be 4 to the fourth and 6 to the fourth

Answer 22

I knew there was a typo! So are you all good now?

Answer 23

Yes I think it would be D I don't know if I'm correct though

Answer 24

@mathmate

Answer 25

To avoid communication errors, please give me the answer and not the letter.

Answer 26

Oh okay sorry ^-^

Answer 27

6 to the fourth

Answer 28

You said that repeating decimals can be turned into fractions and A and B are both repeating

Answer 29

And 4 to the fourth is 2

Answer 30

You there?

Answer 31

@mathmate

Answer 32

Hello?

Answer 33

@campbell_st

Answer 34

well pi is irrational.... so dividing it by anything results in an irrational number.

Answer 35

Oh sorry

Answer 36

I mistyped earlier

Answer 37

4 and 6 are supposed to be put to the fourth

Answer 38

that's ok... I think there are 2 irrational numbers in your answer choices... they both involve pi...

Answer 39

Yeah as I said C and D aren't supposed to have Pi

Answer 40

They're supposed to be put to the fourth

Answer 41

can you use the draw function to write them

Answer 42

\[\sqrt{4} \sqrt{6}\]

Answer 43

I'll let @mathmate continue to answer this

Answer 44

@TwiztTiez
Remember that all integers are rational, because 5 is the same as 5/1, so it can be represented by a fraction.
So the 4 choices are:
1.44444444..... (or 1.4 with a rep. dec. bar)
1/3
4^6
6^6
?
That's why I prefer dealing with the actual numbers, not the choice letters.

Answer 45

or rather
1.44444444..... (or 1.4 with a rep. dec. bar)
1/3
4^6
\(\sqrt4 \sqrt6\) which is the same as \(\sqrt{24}\)

Answer 46

Which one of these can you NOT represent by a fraction?

Answer 47

I didn't mean for it to look like they were supposed to multiplied sorry

Answer 48

That's ok, the multiplication is understood. I just used the law of exponents to simplify it.

Answer 49

Well \[\sqrt{4} =2\]

Answer 50

For your information 1.4444444... equals 13/9.

Answer 51

Very good start, continue!
So
\(\sqrt{4}\sqrt6=2\sqrt{6}\)
can you go further?

Answer 52

Yup yup

Answer 53

I'll put it this way, can you represent \(\sqrt6\) by a fraction?

Answer 54

4.8989794

Answer 55

...mathematically exactly?

Answer 56

\[2\sqrt{6}=4.8989794...\]

Answer 57

2.449489742783178.... and this is not exact.

Answer 58

4.898979485566356... and this is not exact.

Answer 59

Well how can I make it exact? Is there a way or am I just being oblivious?

Answer 60

And I don't mean that rudely

Answer 61

Sorry if it came off that way

Answer 62

Well, there is no way to represent a square root in decimal form unless it is a perfect square. What does that mean (in the context of this question)?

Answer 63

4.89897948556635619639456814941178278393189496131334025686539... and this is still not exact!

Answer 64

Oh okay so

Answer 65

\[\sqrt{4}=2\]

Answer 66

That's exact right?

Answer 67

yes, sqrt(4) is rational.

Answer 68

Okay I get it

Answer 69

but is sqrt(6)?

Answer 70

It can be proved mathematically that square root of a number (such as 2, 3, 5,6,...) is not rational unless the number is a perfect square (1,4,9,16,25....)

Answer 71

2.44948974278

Answer 72

So no I don't think so

Answer 73

You can read more about it (and it is interesting reading for general information) at, for example, Wiki:
http://en.wikipedia.org/wiki/Irrational_number
or
http://www.purplemath.com/modules/numtypes.htm

Answer 74

Thanks!

Answer 75

Correct, since sqrt(6) is not rational, so 2sqrt(6) is also not rational.
Does that clear things up a little?

Answer 76

It does thanks for the help!

Answer 77

Good, you're welcome! :)