Question

How do you write \[0.0125\] in fraction form ?

Answer 1

Hint:
In this we are given a decimal \[0.0125\] and we are asked to write it as a fraction. So while approaching this question we need to keep in mind about the decimal numbers and the fractional numbers. The decimal numbers that can be defined as the form of the number in which it contains a whole number and the decimal part after the dot or point which is known as decimal point. Now a fractional numbers are the numbers of the form \[\dfrac{p}{q}\] where \[p\] and \[q\] both are real numbers can be negative and positive where \[p\] and \[q\] cannot be zero.

Complete step by step solution:
Here in this question we are given a decimal number\[0.0125\] (a decimal number can be defined as the form of the number in which it contains a whole number and the decimal part after the dot or point which is known as decimal point. Also the term after the decimal point can be repeating or non-repeating) and we are asked to how to write it as a fraction (the numbers of the form \[\dfrac{p}{q}\]where \[p\]and \[q\]both are real numbers can be negative and positive where \[p\]and \[q\]cannot be zero and the\[p\] is numerator and\[q\] is the denominator)
So for converting the decimal into a fraction we need to remove the decimal point first by dividing the number of the similar power of the \[10\] as the number after the decimal point that is depicted as –
\[0.0125 = \dfrac{{125}}{{1000}}\](Placed \[{10^4}\] only in the denominator as there is four digit after the decimal point)
Now simplifying the above fraction further that is as follows –
\[
  \dfrac{{125}}{{1000}} \\
   = \dfrac{5}{{40}} \\
   = \dfrac{1}{8} \\
 \]

As the above fraction \[ = \dfrac{1}{8}\] is the best simplified form that is desired so there cannot be more further simplification that is the required fraction of the given decimal in the question \[0.0125\] is \[ = \dfrac{1}{8}\]

Note:
While solving such kind of question one should have a detailed knowledge of decimal part and decimal representation and about the fractions and the types of fractions also that is equivalent fraction, proper fraction (in which the numerator is inferior to the denominator), improper fraction (in this the numerator is greater than denominator), mixed fraction (the type of the fractional numbers which consist of a whole part and a fractional part of the number that is of the form \[t\dfrac{p}{q}\] where \[t\] is the whole number part and the \[\dfrac{p}{q}\] is the fractional part ). The calculations here are needed to be done with concentration when the removal of the decimal point and the simplification of the fraction is done as the whole question depends on the precision of the answer.