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.
So 3 in every 10 would make it because 30% equals 3/10 and since there are 50 that would be 5 sets of 10. Thus 3*5=15. You would make 15 shots
Answer:
Step-by-step explanation:
In the equation of a straight line (when the equation is written as "y = mx + b"), the slope is the number "m" that is multiplied on the x, and "b" is the y-intercept (that is, the point where the line crosses the vertical y-axis).
Answer:
Quadrilateral ABCD does not map onto itself using a reflection because it has 0 lines of symmetry.
Step-by-step explanation:
Remember that a trapezoid has no lines of symmetry.
Answer:
D
Step-by-step explanation:
Mathematically, the mid segment of a trapezoid is exactly the average of the 2 parallel bases
What this means is that to find the length of the trapezoid, we will need to find the average of the two parallel bases
Mathematically, this is same as adding the two bases and dividing the result by 2.
Hence we can say it is exactly one-half the length of the sum of the two parallel bases
