what does a irrational number look like

Answers

Answer 1

A irrational number is a number that can't be expressed as a ratio of two whole numbers. That's it.

For examples (in increasing order of difficulty)

1 is a rational number because it is 1/1

0.75 is a rational number because it is equal to 3/4

2.333... (infinite number of digits, all equal to three) is rational because it is equal to 7/3.

sqrt(2) is not a rational number. This is not completely trivial to show but there are some relatively simple proofs of this fact. It's been known since the greek.

pi is irrational. This is much more complicated and is a result from 19th century.

As you see, there is absolutely no mention of the digits in the definition or in the proofs I presented.

Now the result that you probably hear about and wanted to remember (slightly incorrectly) is that a number is rational if and only if its decimal expansion is eventually periodic. What does it mean ?

Take, 5/700 and write it in decimal expansion. It is 0.0057142857142857.. As you can see the pattern "571428" is repeating in the the digits. That's what it means to have an eventually periodic decimal expansion. The length of the pattern can be anything, but as long as there is a repeating pattern, the number is rational and vice versa.

As a consequence, sqrt(2) does not have a periodic decimal expansion. So it has an infinite number of digits but moreover, the digits do not form any easy repeating pattern.


Related Questions

Can someone help me please

Answers

Answer:

height of b = 280

Step-by-step explanation:

candle b has a height of 280 - 5t, when it comes out of the mold then t=0 so the initial height of b is 280

candle b's height drops by 5 every hour (that's what the -5t part means)

candle a started at 216 and dropped to 192 in 3 hours, so it dropped by 24 in 3 hours so it drops 8 each hour

so candle b starts out taller (280 v. 216) and candle b burns slower (a at 8 per hour and b at 5 per hour), so b will never 'catch up' with a... candle a will be burned out while candle b is still burning

PLSSSSSSSS HELP CORRECT ANSWER GETS BRAINLIEST
Answers
A.2 bags
B.3 bags
C.4 bags
D.5 bags

Answers

Answer:

A. 2 bags

Step-by-step explanation:

12x5=60

60 divided by 2 = 30

30 divided by 15 equals 2 bags

Please tell me if this is correct or incorrect  

Hope this helps

Step-by-step explanation:

what are the dimensions of the flower bed

otherwise you can solve it by 151515/area of the flower bed

need help , ill give a brainlist to the best answer ​

Answers

Answer:

-7, 7

Step-by-step explanation:

10 - 4 (3-2y) = 8y -5

Answers

Answer:

No Solutions

Step-by-step explanation:

10 - 4(3-2y) = 8y - 5

Distribute:

10 - 12 + 8y = 8y - 5

Simplify:

-2 + 8y = 8y - 5

Same to both sides

-2 + 5 = 8y - 8y

3 = 0y

No Solutions

Let me know if you have any questions

A student solves the inequality −5v>55. Each step in the student's solution is shown below. Identify where the student made any errors.

Answers

Note: Steps of student are not given. So, the proper steps of the solution are provided below.

Given:

The inequality is

[tex]-5v>55[/tex]

To find:

Where the student made any errors?

Solution:

We have,

[tex]-5v>55[/tex]

On dividing both sides -5 change the sign of equality because -5 is a negative number.

[tex]\dfrac{-5v}{-5}<\dfrac{55}{-5}[/tex]

[tex]v<-11[/tex]

Therefore, the solution of given inequality is [tex]v<-11[/tex].

Rewrite this division expression a an equivalent multiplication expression: 5/8 divided by 2/3

Please help me I’m not very smart lol

Answers

Answer:

Step-by-step explanation:

Dividing by a fraction is the same as multiplying by the upside-down fraction.

(5/8) ÷ (2/3) = (5/8) ⋅ (3/2) = 15/16

asdfruhyhkijgfdsafuhyfjtfrdef

Answers

Answer:

Epic

Step-by-step explanation:

stop random spam(thanks for points xD)

1/3a = -5. Solve each equation

Answers

Answer:

1/3a = -5

1=3a×-5

1=-15a

a=-1/15

Answer:

a=-15

Step-by-step explanation:

1/3a = -5

1/3(*3)a=-5*3

a=-15

3 unit right
3 unit left
3 unit up
3 unit down

8 unit right
8 unit left
8 unit up
8 unit down

Answers

The answer to your question is 3 units to the right and 8 units down.

1/4 of the soda was left. If you wanted to split the soda equally to 5 people, how much soda will each person get?

Answers

Answer:

1/20 of the soda

There are 6 balls. Half of the balls are blue. One ball is red. The rest are green. Write the fraction for the green balls.

Answers

2/6 of the balls are green or 1/3

Answer:

1/3 (Minimized) 2/6

Step-by-step explanation:

Select the correct answer.
What is the simplified form of V45?
OA. 15
OB. 19.5
O c. 35
OD. 53

Answers

Answer:

C. 3√5

Step-by-step explanation:

45 = 3 × 3 × 5 considering this the answer is C

Answer:

c

Step-by-step explanation:

HELP meeeeeeeeeeeeeeeeeeeee

Answers

Answer:

first:

a)

second:

b)

Step-by-step explanation:

A andddddddddd b......

Find the area of this obtuse triangle​

Answers

The correct answer is 49!



Which number line shows all the values of that make the inequality -3 +1 < 7 true?

Answers

Answer:

Number line D is true

Step-by-step explanation:

Given

[tex]-3x + 1 < 7[/tex]

See attachment for number lines

Required

Which number line makes the inequality true

First, we solve for x in [tex]-3x + 1 < 7[/tex]

[tex]-3x < 7 - 1[/tex]

[tex]-3x < 6[/tex]

Divide through by -3

[tex]\frac{-3x}{-3} < \frac{6}{-3}[/tex]

[tex]x > -2[/tex]

The inequality means x is greater than -2.

This means that, the line must point to the right of -2 and the "greater than" means that the circle must be opened

Number line D is true

NO WRONG ANSWERS !!! Evaluate 501 × 502​

Answers

Answer:

251,502

Step-by-step explanation:

hope it helps!

....

Answer:

501 × 502 = 251,502

...

The Value that you insert into a function is know as the?

Answers

Answer:

Step-by-step explanation:

Most commonly, that value would be the "independent variable."

We evaluate the function at that particular value of the independent variable.

!!!!!PLEASE HELP MEEEEE!!!!!

Answers

Answer:

c hehhe

Step-by-step explanation:

5= h/1.25 help me plz

Answers

Answer:

Step-by-step explanation:

5=h/1.25

h=6.25

On solving for the value of {h}, we get -

{h} = 6.25.

What is function?

A function is a relation between a dependent and independent variable. We can write the examples of functions as -

y = f(x) = ax + b

y = f(x, y, z) = ax + by + cz

Given is the expression as -

5 = h/1.25

We can solve for the value of {h} as -

5 = h/1.25

{h} = 5 x 1.25

{h} = 5 x 125/100

{h} = 125/20

{h} = 6.25

Therefore, on solving for the value of {h}, we get -

{h} = 6.25.

To solve more questions on functions, visit the link below-

https://brainly.com/question/30194223

#SPJ2

Write an equation of the parabola in intercept form that passes through (-2, 0.05) with x-intercepts of -7 and -3

Answers

Important things you need to know:

1. x intercept = solution of the equation

2. parabola = the highest power is x²

3. "passes through" is important because you have the y intercept (it is the c in ax² + bx + c = 0)

The intercept form is y = a(x-r)(x-s), where r and s are the x intercepts (solutions) of the graph

Substitite the numbers and values you know:

y = a(x-r)(x-s)

0.05 = a(-2-(-7)) × (-2-(-3))

Then you should find a.

Rewrite the equation in the form of y = a ( x+7 )( x+3 ) where the value of a is found.

A local aquarium purchased a new turtle tank for their giant turtle exhibit. What is the volume of the turtle tank?

Answers

Answer:

[tex]Volume = 1440m^3[/tex]

Step-by-step explanation:

Given

Missing dimensions:

[tex]Length = 15m[/tex]

[tex]Width = 8m[/tex]

[tex]Height = 12m[/tex]

Required

Determine the volume

Volume is calculated as:

[tex]Volume = Length * Width * Height[/tex]

This gives:

[tex]Volume = 15m * 8m * 12m[/tex]

[tex]Volume = 1440m^3[/tex]  

la altura del muro en el que se encuentra el tanque es:​

Answers

Answer:

3m•sen(60°) es la respuesta

math question file down below

Answers

30 + 2(n)

30 + 2(10) = $50

30 + 2(18) = $66

30 + 2(24) = $78

Suppose that the function f(x)=3x+10 represents the cost to rent a movie for a month. Kim has $15. How many more dollars does she need to rent 8 movies?

Answers

Answer:

$19

Step-by-step explanation:

Given data

Cost of movie

f(x)=3x+10

Hence the cost of 8 movies is

f(x)=3(8)+10

f(x)=24+10

f(x)=$34

Hence the cost of 8 movies is $34, Kim needs extra

=34-15

=$19

When a new TV became available in a store, the number sold in the first week was high. Sales
decreased over the next two weeks and then they remained steady over the next two weeks. The
following week, the total number sold by the store increased slightly. Sketch the graph of this function
over the six weeks.

Answers

Answer:

The way you would sketch the graph is slowly increasing, staying about the same, and then go up a little bit.

Good luck!

Tracy purchases cotton candy in a ratio of 2 pink to 7 blue to sell at a carnival. She has a total of 108 bags. How many bags of each color does she have?

Answers

Answer:

24 pink

84 blue

Step-by-step explanation:

2 + 7 =9

2/9 = x/108

108 ÷ 9 = 12

12 × 2 =24

24 pink

7/9 = x/108

108÷9 = 12

12 ×7 =84

84 blue

What is additive inverse of the check?
please help



7x -3




-7x + 3



-7x - 3



7x - 3

Answers

Answer:

pretty sure it would be 7x-3

Connections Academy Sample Work Pre Calc
Please Help!!!
I believe
y (theta) = 3 sin t
and
a(theta) = 3 cos t
but that might be wrong because I'm so confused. Please Please help!

Answers

Step-by-step explanation:

sintheta=y/3"

theta=sin-¹(y/3")

cos theta=a/3"

theta=cos-1(a/3)

sin beta=y/7"

beta=sin-¹(y/7")

b=√{y²+7" ²}

sorry last one I don't know

Answer:

sinθ = y/3                        ⇒ y(θ) = 3 sinθcosθ = a/3                       ⇒ a(θ) = 3 cosθsin β = y/7 = 3 sinθ / 7    ⇒ β(θ) = arcsin (3/7sinθ)b(θ) = √(7²-y²) = √(49-9sin²θ)p(θ) = a(θ) + b(θ) = 3 cosθ + √(49-9sin²θ)

The graph is attached

---------------------------------------

p.s.

b(θ) can be put in different way:

cos β = b/7 ⇒ b(θ) = 7 cos β = 7cos(arcsin(3/7sinθ))

Then

p(θ) = a(θ) + b(θ) = 3 cosθ + 7cos(arcsin(3/7sinθ))

This doesn't change the function or the graph

Write the equation in point-slope form given the following information: f(3)=7 and f(8)=17

Answers

Answer:

Point-slope is the general form y-y₁=m(x-x₁) for linear equations. It emphasizes the slope of the line and a point on the line (that is not the y-intercept).

Step-by-step explanation:

Brainly needs at least 20 characters.

if there are 10 birds for 4 dogs,what is the ratio of birds to dogs?

Answers

Answer:

10:4 ( Answer )

I hope it helps you

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