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oksano4ka [1.4K]
2 years ago
10

What does a irrational number look like

Mathematics
1 answer:
julia-pushkina [17]2 years ago
5 0

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.

You might be interested in
6th grade math help me please :))
sergij07 [2.7K]

Answer:

The answer is option D.

3u + 1 + 7y

All the terms here are different and cannot be combined

Hope this helps you

4 0
3 years ago
Given an arithmetic sequence in the table below, create the explicit formula and list any restrictions to the domain.
djyliett [7]
An=a1+d(n-1)
an=nth term
a1=first term, when n=1
d=common differnce=amount each term increases by
n=which one


so
when n=1, an=40
so a1=40
it seems to increas by 7 each time

an=40+7(n-1)
explicit formula is expanded
an=40+7n-7
an=33+7n is the formula

the domain is natural numbers because you can't have the -3rd term or the 0th term or the 3.24th term

domain is natural numbers
the formula is a_n=33+7n or a_n=7n+33
6 0
3 years ago
What is the value of x in the triangle?
yulyashka [42]
<h3>Answer: C) x = 13</h3>

====================================================

Work Shown:

We have a right triangle with legs a = 5 and b = 12. The hypotenuse is c = x which is unknown for now.

Use the pythagorean theorem to find x.

a^2 + b^2 = c^2

5^2 + 12^2 = x^2

25 + 144 = x^2

169 = x^2

x^2 = 169

x = sqrt(169)  .... apply the square root to both sides

x = 13

4 0
3 years ago
Chelsey put for $450 into an account with a simple interest rate of 2.5% when she withdrew the money she had earned a total of $
fgiga [73]

Answer:

5.66 years

Step-by-step explanation:

450 x 1.025^(n) = 450 + 67.50

450 x 1.025^(n) = 517.50

1.025^(n) =(517.50 / 450)

1.025^(n) = 1.15

n = ln(1.15) / ln(1.025)

n = 5.66

6 0
3 years ago
10.Which of the following values does not satisfy the inequality ?
kupik [55]

Answer:

The answer is -4

Step-by-step explanation:

-2x-6<=1

-2(-4)-6<=1

8-6<=1

2<=1 which is False

-2x-6<=1

-2(-3)-6<=1

6-6<=1

0<=1 which is True

-2x-6<=1

-2(-2)-6<=1

4-6<=1

-2<=1 which is True

-2x-6<=1

-2(-1)-6<=1

2-6<=1

-4<=1 which is True

7 0
3 years ago
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