Question

. Given the following set of numbers, circle each irrational number (there may be more than one). a. 23 b. √ 3 c. 휋 d. 0 e. − 6 . 55555 f. 4 9 g. - 2 h. 3.14 Explain how you know the set above are ir rational numbers . ______________________________________________________________ _______ _____________ ______________________________________________________________ _______ _____________

Answer 1

An irrational number is a number that can not be written in fractions.

A non-terminating non-repeating decimal is an irrational number.

Fractions is a number that have some number in numerator (on the top) and some number in denominator (bottom) , e. g. 3/4, 2/1, 5/7....

In the given list of numbers, we need to check which number is an irrational number, i.e. it can not be written in fraction form.

a. 23 : 23 is a whole number and every whole number could be written in the for of a rational number. 23 could be written as 23/1. So, it's a rational number.

b. √ 3 : If we convert it in decimal form, we would get a non terminating decimal number. √ 3 = 1.732..... because it's a non terminating non-repeating decimal, we could say, √ 3 is an irrational number.

c. : Option C is not clear

d. 0 : Zero could be written as a fraction 0/1 . So, it's a rational number.

e. − 6 . 55555 : It is a non terminating but repeating decimal, we could say, − 6 . 55555 is a rational number.

f. 49 : 49 could be written as 49/1. So, it's a rational number.

g. - 2 : -2 could be written as -2/1. So it's also a rational number.

h. 3.14 : 3.14 could be written as 314/100 after removing decimal because 3.14 is the decimal upto hundredth place. So, 3.14 is also a rational number.