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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.

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jeka94

Answer:

Vertical angle congruence theorem

3 0
3 years ago
Nick made his histogram showing the number of sport caps each of his friends own.
pickupchik [31]

Answer:

A. 7

Step-by-step explanation:

2 or 3 caps = 13

6 or 7 caps = 6

13 - 6 = 7

- hope this helps! -

3 0
2 years ago
At a soccer tournament 12 teams are wearing red shirts, 6 teams are wearing blue shirts, 4 teams are wearing orange shirts and 2
earnstyle [38]

Answer:

24 blank shirts

Step-by-step explanation:

I'm guessing you're asking for blank shirts. 12+6+4+2=24. 24 teams so far, but there are the blank shirts.

(24+b)/2=b. Multiply by 2

=24+b=2b. Subtract b

24=b

8 0
3 years ago
Can someone tell me the answer
astra-53 [7]

Answer:

-3

Step-by-step explanation:

(-6)/(+2)

-6/+2

-3

5 0
3 years ago
Read 2 more answers
What’s the correct answer for this?
grigory [225]

Answer:

The answer is 20

Step-by-step explanation:

Reasoning it is correct because for questions like this the bottom numbers for each shape are 10 and 8 they are very close to each other on the number line there fore since the number is two off you subtract 2 and then two again since it is 2 off to get 21 the closest answer is 20

It is a little confusing but since it is two places off you subtract two twice

8 0
3 years ago
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