Question

Classify each number as rational or irrational. Drag the choices into the boxes to correctly complete the table. rational irrational

Answer 1

Step-by-step explanation:

1. 0.167 irrational
2. 2/9 rational
3. π irrational
4. 255 rational

Answer 2

The first, second, and fourth values are rational whereas the third value "pi" is an irrational number.

Irrational and Rational Numbers  from decimal representation :

• Terminating decimals i.e. the ones that end with a zero reminder like '7.25' are rational.
• Non-terminating but recurring decimals like '2.666666...' have a repetitive sequence of decimal digits and are also rational
• Non-terminating as well as non-recurring or repeating decimals i.e. never-ending no-sequence decimals are irrational in nature.

1. 0.167167167....

• Here, the decimal is non terminating i.e. endless
• Also the decimal digits from a repeating pattern of "167".
• Thus, it is a nonterminating and recurring decimal i.e. Rational

2. 2/9

• 2/9 in decimal representation is 0.22222222.....
• Here, the decimal is non terminating i.e. endless
• Also the decimal digits from a repeating pattern of "2".
• Thus, it is a nonterminating and recurring decimal i.e. Rational

3. π i.e. pi

• The decimal representation of π is 0.314159265359
• Here, the decimal is non terminating i.e. endless
• But there is no pattern of repeating in the decimal digits as 1 is followed once by 4 and then 5.
• Thus, it is a nonterminating and nonrecurring decimal i.e. Irrational

4. $\sqrt{ 225}$

• The decimal representation of $\sqrt{225} = 15.0$
• Here, the decimal is terminating as it is an integer and the division ends with a zero remainder.
• Thus, is a terminating decimal i.e. Rational

Hence, 0.167.., 2/9, and root(225) are rational numbers and 'pi' is an irrational number.

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