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.
Answer:
15 minutes??
I guess?
Step-by-step explanation:
Im really not sure
There's a pattern!!
You just need to count how many numbers passed by!
Clear?
Answer: So lets say that the width is w. The length(L) is 4 meters greater than 3 times the width. 3 times the width would be 3w, and then 4 meters greater than that would be 3w+4. You have two widths and two lengths to a rectangle that must add up to equal 72. So 2w + 2L =72. But remember that one L equals 3w+4
2(w) + 2(3w+4) = 72
2w+6w+8=72
8w+8=72
8w=64
w=8
L=3w+4
L=3(8)+4
L=24+4
L=28
So the dimensions are 8 meters by 28 meters
To check 2(8)+2(28)=72
Answer:
Step-by-step explanation:
∩ 
is asking for the intersection of sets 
and , or simply, which numbers can be found in both sets.
The numbers shared between the two sets are 
.
Next, we need to union this result with the set 
, or simply, combine the numbers in both sets together.
This would result in 
Answer:
5t+3
Step-by-step explanation:
1 Collect like terms.
(7t-2t)+3
2 Simplify.
5t+3
