Which number is irrational?

Responses

A. 1.01001000100001.....

B. 1.2525252525.....

C. √100

D. 4 1/6

A. 1.01001000100001.....

thank you

The number that is irrational is option C, √100.

The irrational numbers are numbers that cannot be expressed as a fraction (i.e., not rational) and do not terminate or repeat their decimal representation.

To determine which number in the given options is irrational, we need to examine each option and check for the conditions of irrationality.

A. The number 1.01001000100001... appears to be a repeating decimal, with the pattern being the sequence of 1s followed by increasing numbers of zeros. Therefore, it is not an irrational number.

B. The number 1.2525252525... repeats the pattern of the digits 25. Since it repeats its decimal digits, it is also not an irrational number.

C. The square root of 100 (√100) can be calculated as 10 because 10 * 10 = 100. Since √100 can be expressed as a whole number, it is not an irrational number.

D. The number 4 1/6 can be written as the fraction 25/6, which is a rational number since it can be expressed as a ratio of two integers.

Based on the analysis above, none of the given options are irrational numbers.