Question

find an irrational between 1/7and 2/7​

Answer 1

Answer:

Here’s another method to find an irrational number between two rational numbers

Square your lower number: (1/7)² = 0.0204081634

(round it UP just in case the calculator rounded the number down)

Square your higher number: (2/7)² = 0.0816326530

(round it down just in case the calculator rounded the number up)

Pick ANY decimal number between these two numbers, but be sure the number ends in 2, 3, 7 or 8, so we don’t accidentally pick a perfect square.

There is a calculator method of picking these random numbers.

(see further below)

I manually erased any answers that ended in 0, 1, 4, 5, 6, or 9 because there is a tiny chance that those numbers might be perfect squares. There is absolutely zero chance that any of these numbers are perfect squares.

Step-by-step explanation:

I defined A and B equal to the squares of our two given numbers

I did not need to round these (just in case) because the calculator rounds its numbers in memory to 14 digits of precision.

Each of the other lines uses rand (a random number between 0 and 1) to generate a random number between A and B.

The square roots of these four sample numbers are all irrational because I manually erased (Clear) any number ending in 0, 1, 4, 5, 6, or 9.

Irrational Values between 1/7 and 2/7: 0.0239431427−−−−−−−−−−−√,0.0745281463−−−−−−−−−−−√,0.0730254898−−−−−−−−−−−√,0.0787288242−−−−−−−−−−−√

Feel free to steal my trick. There are many other methods.

Here’s another method:

Pick any number between 1 and 4 (the squares of the numerators) that ends in 2, 3, 7 or 8.

Or pick numbers that end with those digits as long as you are sure they are not perfect squares (like 2 and 3 or 1.9 or 2.5.)

Write a fraction with the square root of the number you just chose in the numerator, and keep the same denominator.

For example: 1.9√7,sqrt2.57and2.22222222√7 are all between 1/7 and 2/7.

ANOTHER TRICK

Add a very small irrational number to the smaller number

Subtract a very small irrational number from the larger number

17+e1000or27–π10000