Which number is irrational?
a
\large \sqrt{81}
b
3.898989...
c
-3/4
d
\large \frac{2\pi}{7}
b
The number that is irrational is \(\frac{2\pi}{7}\) (option d).
To determine which number is irrational among the given options, we need to understand what an irrational number is. An irrational number is a real number that cannot be expressed as a fraction (ratio) of two integers. In other words, it cannot be written in the form a/b, where a and b are integers and b is not equal to zero.
Let's analyze each option to identify the irrational number:
a) √81: This can be simplified to 9, which is a rational number since it can be expressed as 9/1.
b) 3.898989...: This repeating decimal can be converted into a fraction. Let x = 3.898989...,
then 100x = 389.898989...,
subtracting x from 100x gives us 99x = 389,
so x = 389/99. Therefore, this number is a rational number.
c) -3/4: This is a rational number since it can be expressed as a fraction.
d) 2π/7: π (pi) is an irrational number, and any non-zero constant multiplied by an irrational number remains irrational. Therefore, 2π/7 is also an irrational number.
Hence, the answer is option d) 2π/7, which is irrational.