Rational and Irrational Numbers

Our current number system, the Hindu-Arabic numeral system, was developed because humans required an efficient way to represent the quantities they were working with.

Several mathematicians from India are credited with the development of the place-value system and the introduction of the number zero in the 5th and 6th centuries.

Represent each of the following place values as a power of $10$.

Represent the following rational number as a fraction in simplified form.

$7.40111...$

Represent the following rational number as a fraction in simplified form.

$3.0\overline{43}$

Represent the following rational number as a fraction in simplified form.

$-0.862$

Represent the following rational number as a fraction in simplified form.

$2.4111...$

Represent the following rational number as a fraction in simplified form.

$2.\overline{4}$

Represent the following rational number as a fraction in simplified form.

$3.1$

Represent the following rational number as a fraction in simplified form.

Represent the following rational number as a fraction in simplified form.

$0.222...$

Classify the following number as either rational or irrational. Justify your answer.

$18$

Classify the following number as either rational or irrational. Justify your answer.

$\sqrt{49}$

Classify the following number as either rational or irrational. Justify your answer.

$8.7255555....$

Classify the following number as either rational or irrational. Justify your answer.

$33.\overline{914}$

Classify the following number as either rational or irrational. Justify your answer.

$\sqrt{17}$

Classify the following number as either rational or irrational. Justify your answer.

$7.68$

Classify the following number as either rational or irrational. Justify your answer.

$\mathrm{\pi }$

Classify the following number as either rational or irrational. Justify your answer.

$\frac{2}{3}$

Classify following number as either rational or irrational. Justify your answer.

$0$

Classify following number as either rational or irrational. Justify your answer.

$19.34862147...$

Classify following number as either rational or irrational. Justify your answer.

$\sqrt{81}$