Introduction: Rational Numbers

Q.

Classify the following numbers as rational or irrational:

$2\pi$

Q.

Can we show that$0.01001000100001......$ is an irrational number using the contradiction method?

Q.

Every integer is a rational number

1. True
2. False

Q.

State whether the following statement is true or false: Some real numbers are rational numbers.

1. True
2. False

Q. Convert the following common fraction into decimal fraction.
$\frac{1}{25}$

Q.

State Whether The Following Statement Is True Or False. Every Rational Number Is A Whole Number.

1. True
2. False

Q. Sort the following number types in the increasing order of their quantity from top to bottom.

1. Natural numbers
2. Integers
3. Rational numbers
4. Whole numbers

Q. The rational of the form 'p/q' can be a fraction if 'q' is a/an _________.

1. integer
2. whole number
3. rational number
4. natural number

Q. a : b is the representation of a fraction.

1. True
2. False

Q. Represent the following mixed infinite decimal periodic fractions as common fractions:
Simplify the following expressions.
$\frac{a+b}{a^{2/3}-a^{1/3}{b}^{1/3}+b^{2/3}}-\frac{a-b}{a^{2/3}+a^{1/3}{b}^{1/3}{b}^{2/3}}-\frac{a^{2/3}-b^{2/3}}{a^{1/3}-b^{1/3}}\cdot$

Q.

If $\frac{x}{y}$ and $\frac{y}{x}$ are rational numbers, then which of the following options is correct?

1. $x\ne 0,y\ne 0$

2. $x$ can be 0, $y\ne 0$

3. $x\ne 0$, y can be 0

4. Both $x$ and $y$ can be 0.

Q.

Q. whatf fraction of a dozen is 5?