Exercise 6 Page 16

Classify 4.27

Note that the symbol on top of the digit 7 means that this number is repeated indefinitely. 4.27=4.2 7 7 7 7 7... The number has infinitely many digits after the decimal symbol. Furthermore, these digits repeat themselves indefinitely. This means that the number is a repeating decimal number. Consequently, it can be written as the ratio of two integers. We can conclude that the first number is a rational number.

Classify 0.375

To categorize 0.375 we will consider whether we can express the number as the ratio of two integers. 0.375 = 375/1000 Since 375 and 1000 are both integers we can express 0.375 as a ratio of two integers, so this number is rational.

Classify 0.232342345...

We know that the dots at the end mean that the number continues indefinitely. 0.232342345... The number has infinitely many digits after the decimal point. Furthermore, these digits do not follow a specific pattern. This means that they neither terminate nor repeat. Consequently, the number cannot be written as a ratio of two integers. Therefore, we can conclude that the this number is an irrational number.

Classify sqrt(62)

Classify - 131

Next, we will think whether the last number is a rational number or an irrational number. - 13/1 ⇔ - 13/1 Since - 13 and 1 are both integers, we can express - 131 as a ratio of two integers, so this number is a rational number.