Question

The fractional value of \[0.125\] is
A.\[\dfrac{1}{8}\]
B.\[\dfrac{{23}}{{999}}\]
C.\[\dfrac{{61}}{{550}}\]
D.None of these

Answer 1

Hint: First, we will remove the decimal point before creating a fraction by multiplying both the numerator and denominator with 100. Then we will divide the fractions unless the numerator or the denominator cannot be divided further.

Complete step-by-step answer:
We are given that the decimal number is \[0.125\].
We know that we have to remove the decimal point before creating a fraction by multiplying both the numerator and denominator with 100.
Rewriting the given number, we get
\[
   \Rightarrow \dfrac{{0.125 \times 1000}}{{1 \times 1000}} \\
   \Rightarrow \dfrac{{125}}{{1000}} \\
 \]
But we know that the above fraction is not in the simplest form that the fraction could be in.
Dividing the numerator and denominator of the above fraction by 5, we get
\[
   \Rightarrow \dfrac{{125 \div 5}}{{1000 \div 5}} \\
   \Rightarrow \dfrac{{25}}{{200}} \\
 \]
Dividing the numerator and denominator of the above fraction by 5 again, we get
\[
   \Rightarrow \dfrac{{25 \div 5}}{{200 \div 5}} \\
   \Rightarrow \dfrac{5}{{40}} \\
 \]
Now we will divide the numerator and denominator of the above fraction by 5 again, we get
\[
   \Rightarrow \dfrac{{5 \div 5}}{{40 \div 5}} \\
   \Rightarrow \dfrac{1}{8} \\
 \]
Since the numerator is 1, the above fraction cannot be simplified further.
Therefore, the answer in its simplest form is \[\dfrac{1}{8}\].
Hence, option A is correct.

Note: We know that a rational number is a number that can expressed as the quotient or fraction of two integers, that is, \[\dfrac{p}{q}\] where \[p\] and \[q\] are integers and \[q\] is not equal to zero. We need to know that the rational numbers are closed under addition, multiplication and division, but not closed under subtraction. So we can divide the numerator and denominator by the same number and it won’t affect the fraction. We will not divide the numerator and denominator with different numbers as it will lead to wrong answers.