an irrational number between ⅔ and ½
Answers
Answer:
A rational number is defined as any number that can be written as a fraction in the form ab . Something such as π10 would be irrational, since it can’t be written as ab . Sure, π10 is a fraction like ab , but in that fraction, a=π . The two numbers a and b must be non-zero integers (well, at least b , since dividing by zero is indeterminate) for it to be a rational number. Another way to say this is that a rational number is a number that can be written out as either a terminating decimal or a repeating decimal. Something like π or e or 2–√ written out never ends, but unlike a repeating decimal (for example, 13 ), it never repeats itself. Therefore, it cannot be written out as a fraction either.
There are infinitely many rational numbers between 12 (or 0.5 ) and 13 (or 0.3¯ ), since you can use as many decimal places as you would like to. Here are some examples:
0.50=12
0.49=49100
0.48=1225
0.47=47100
0.46=2350
0.45=920
(I just wanted to point out that writing a decimal as a fraction like this is called “rationalisation,” for obvious reasons.)
Of course, you can increase the number of decimal places and get more rational numbers. Take 0.47 as an example:
0.47=47100
0.407=4071000
0.4007=400710000
0.40007=40007100000
You get the point. And we can continue this forever.
Answer:
An irrational number is a number that can’t be expressed as a ratio of two integers. Since there are infinite numbers between 2 and 3 there are infinite irrational numbers between them. As an example the square roots of all numbers between 4 and 9 will fall between 2 and 3.