Question

Convert \[\dfrac{1}{4}\] to decimals?

Answer 1

Hint: In this question, we need to convert the fractions into decimals. A fractional number is nothing but it is a type of number which is in the form of \[\dfrac{a}{b}\] where \[b\neq 0\] , \[a\] and \[b\] are whole numbers. Mathematically there are three types of fractions namely proper fraction ,improper fraction and mixed fraction. Here \[\dfrac{1}{4}\] is a proper fraction . A proper fraction is nothing but a fraction numerator will be smaller than the denominator. Here we need to convert the given fraction into decimals. First we need to make the given fraction over \[100\] then by simplifying we can convert the given fraction to decimals.

Complete step by step answer:
Given, \[\dfrac{1}{4}\]
We can make the fraction over \[100\] to make conversion much easier.
By multiplying both the numerator and denominator by \[25\] ,
We get,
\[\Rightarrow \dfrac{1 \times 25}{4 \times 25}\]
By multiplying ,
We get,
\[\Rightarrow \dfrac{25}{100}\]
On simplifying ,
We get,
\[\Rightarrow \ 0.25\] and also \[\dfrac{25}{100} = \dfrac{1}{4}\]
Therefore \[\dfrac{1}{4}\] is also \[0.25\] .
\[\dfrac{1}{4}\] is equal to \[0.25\]

Note: A simple example for decimal numbers is that we can write \[0.5\] instead of writing \[\dfrac{1}{2}\] . We need to know that \[0.5\] is the same as \[\dfrac{5}{10}\] . There is another fraction named improper fraction whose numerator is equal to or greater than its denominator. An example of improper fraction is \[\dfrac{11}{5}\] . We need to know that all fractions are rational numbers but not all rational numbers are fractions. Rational numbers are nothing but the numbers which can be represented in the form of \[\dfrac{p}{q}\] where \[p\] and \[q\] are integers and \[q \neq 0\] . Mathematically, Rational numbers are denoted by Latin capital letter \[Q\] and also rational numbers are included in the real numbers. Basically, rational numbers form a dense subset of the real numbers. We need to know that two different rational numbers may correspond to the same rational number.
Alternative solution :
We can also convert the given fraction into decimals by division method .
Given \[\dfrac{1}{4}\] ,
On dividing \[1\] by \[4\] ,
We get, \[\dfrac{1}{4}=0.25\]
Thus \[\dfrac{1}{4}\] is equal to \[0.25\]