Question

All rational numbers are real numbers.\[\]
A. True \[\]
B. False\[\]

Answer 1

Hint: We recall that a rational is a number that can be expressed in the form $\dfrac{p}{q}$ where $p$ an integer is and $q$ is a non-zero integer. We recall the real number is a number that can be expressed as decimals with finite or infinite numbers of digits.

Complete step-by-step solution:
We know that the rational number is a number that can be expressed in the form $\dfrac{p}{q}$ where $p$an integer is called numerator and $q$ is called the denominator. \[\]
We know that every rational expression can have a decimal representation with the whole integral part or decimal part separated by a decimal point. If the digits after the decimal point are finite then we called the decimal terminating decimal, for example $1.234$. If the digits after the decimal point are infinite or shall we say one or more digits repeat themselves then we called the decimal non-terminating or recurring decimal, for example $1\cdot \overline{2}=1\cdot 222222...$.\[\]
We know that the real numbers are numbers that can be represented as decimals, for example $1.234,1.\overline{2},1.2323323332...$. The decimals which are non-terminating and non-recurring for example $1.2323323332...$ are not rational but irrational numbers.
Since every rational number can be represented in decimal form every rational number is a real number. So the given statement is true. \[\]

Note: We note that the rational numbers are solutions to linear equations $ax+b=0$ where $a,b$ are integers. The irrational number cannot be expressed in the form of $\dfrac{p}{q}$, for example $\sqrt{2},\sqrt{3},5+\sqrt{2}$ et. The real number consists of rational and irrational numbers. The numbers which are not real are called complex numbers and are solutions to the equation ${{x}^{n}}=a$. Complex numbers consist of numbers and imaginary numbers.