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Find a rational and an irrational number between
(2)/(5) and
(3)/(4)

Find a rational and an irrational number between $\frac{2}{5}$ and $\frac{3}{4}$

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Classify rational and irrational numbers

Full solution

Q. Find a rational and an irrational number between

\frac{2}{5}

and

\frac{3}{4}

Convert to decimals: Convert the fractions to decimal form to make it easier to find numbers between them. $\newline$ Calculate $\frac{2}{5}$ and $\frac{3}{4}$ in decimal form. $\newline$ $\frac{2}{5} = 0.4$ $\newline$ $\frac{3}{4} = 0.75$
Find rational number: Find a rational number between $0.4$ and $0.75$ . A simple way to find a rational number between two numbers is to take their average. $(0.4 + 0.75) / 2 = 1.15 / 2 = 0.575$ $0.575$ is a rational number because it can be expressed as a fraction $(575/1000)$ .
Find irrational number: Find an irrational number between $0.4$ and $0.75$ . An irrational number cannot be expressed as a simple fraction. A well-known irrational number is the square root of $2$ , which is approximately $1.414$ . However, we need a number less than $0.75$ . We can use the square root of a non-perfect square that lies between $0.4^2$ and $0.75^2$ . $0.4^2 = 0.16$ $0.75^2 = 0.5625$ We can choose a non-perfect square between $0.16$ and $0.75$ $0$ , for example, $0.75$ $1$ . The square root of $0.75$ $1$ is irrational and lies between $0.4$ and $0.75$ .

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