Question

How do you convert $0.123$ as a fraction $?$

Answer 1

Hint: To solve this question we should know the concept of fraction. We should know to convert the decimal and fraction and vice-versa. Calculation with exponents should also be known to us. To convert the decimal number into fraction we divide the number with${{10}^{n}}$ , like in the case of $0.ab$ when changed to fraction becomes $\dfrac{ab}{100}$ . Calculation with exponents should also be known to us.

Complete step by step answer:
To convert decimal into fraction we need to remove the decimal point from the number. For doing this we need to divide the number from ${{10}^{n}}$ , where $n$ is the position of decimal point. Position of decimal point can be calculated by counting the number of digits to the left of the decimal.
In the given number $0.123$ the decimal is placed at ${{3}^{rd}}$ position from left. To remove the decimal point from this number the value of $n$ here will be$3$, because the decimal point is before $3$ digits from left. So mathematically it can be written as:
$\Rightarrow \dfrac{123}{{{10}^{3}}}$
Now, on expanding the power form in multiplication form, we get:
$\Rightarrow \dfrac{123}{1000}$
$\therefore $ The fraction form of $0.123$ is $\dfrac{123}{1000}$.

Note: The above answer,$\dfrac{123}{1000}$ , cannot be further simplified as $123$ is a prime number and there is no common factor between $123$ and $1000$ , hence the fraction is in its lowest term so it would not be further brought into another fraction.
We can even check whether the fraction for the given decimal is correct or not. To check we will have to remove $1000$ from the denominator and put the decimal point at the ${{n}^{th}}$ position from left where $n$ is the power of the $10$. In this question $n$ is $3$ so the decimal point will be at a position where there are $3$ digits left to the decimal point. On doing this we get $0.123$.
So the fraction $\dfrac{123}{1000}$ when converted to decimal gives $0.123$.