Question

What is the decimal form of the rational number \[\dfrac{23}{8}\] ?

Answer 1

Hint: As we know that rational numbers are those number which are written in the form of \[\dfrac{p}{q}\] where the value of \[q\] must be nonzero and we have given a rational number, to convert this number in decimal form divide the top from bottom to obtain the correct result of the given term.

Complete step-by-step solution:
Whole numbers, natural numbers, and integers are all familiar to us.
Whole numbers are numbers that begin with a zero that is \[0,1,2,3,4,.........\] , therefore natural numbers are also known as whole numbers.
Natural numbers are counting numbers with a finite number of possibilities. The smallest natural number is \[1\].
Integers are the whole integers that fall into the categories of negative, non-negative, positive, and zero.
Rational numbers are one of the most common types of numbers that we study in math after integers. These numbers are in the form \[\dfrac{p}{q}\] , where \[p\] and \[q\] are integers and \[q\] is not equal to zero. Because of the basic structure of numbers, \[\dfrac{p}{q}\] form, most individuals find it difficult to distinguish between fractions and rational numbers. Whole numbers make up fractions, whereas integers make up the numerator and denominator of rational numbers.
If there are no common factors between the dividend and divisor other than one, the standard form of a rational number can be determined, and the divisor is positive.
As a result, a rational number is one that can be expressed as a simple fraction, or as a ratio.
Around \[300\] BC, the Pythagoras in Greece, followers of the famed mathematician and philosopher Pythagoras, were the first to discover non-rational numbers. These numbers are called irrational numbers because they cannot be expressed as a ratio of integers.
Rational numbers' decimal representations either finish or repeat a pattern. Divide the numerator by the denominator to convert fractions to decimals, and if the division doesn't come out evenly, round off after a given number of decimal places.
Now according to the question:
We have given a rational number \[\dfrac{23}{8}\]
To convert this rational number into decimal form divide the numerator by denominator we get:
\[\Rightarrow \dfrac{23}{8}=2.875\]
Hence the decimal form of the given rational number \[\dfrac{23}{8}\] will be \[2.875\] .

Note: Students, you are aware that two German mathematicians, Cantor and Dedekind, demonstrated that: Every real number corresponds to a point on the real number line, and every point on the number line corresponds to a unique real number. The two rational numbers \[\dfrac{a}{b}=\dfrac{c}{d}\] are equal, if \[ad=bc\] .