Question

Convert the following into fractions in their lowest terms: \[2.04\]?

Answer 1

Hint: By the question we can understand that we have to convert the given decimal into a fraction in lowest terms. So, for that first of all we have to convert the given number into fraction and then we have to reduce into lower terms by prime factorization method.

Complete step-by-step answer:
For the given question we are given to convert the decimal number into fraction.
So, let us assume the given number as ‘S’ and consider it as equation (1).
\[S=2.04.............\left( 1 \right)\]
As we can see that the decimal point is at 2 places before in the equation (1).
So, for converting it into fraction we have to eliminate the decimal, for that we have to divide the number by 100, we get
\[\Rightarrow S=\dfrac{204}{100}\]
Let us consider the given equation as equation (2).
\[\Rightarrow S=\dfrac{204}{100}...................\left( 2 \right)\]
Now let us do prime factorization for the numerator and denominator of equation (2), we get
\[\Rightarrow 204={{2}^{2}}\times 3\times 17\]
\[\Rightarrow 100={{2}^{2}}\times {{5}^{2}}\]
Let us consider the above equations as equation (3) and equation (4).
\[\Rightarrow 204={{2}^{2}}\times 3\times 17................\left( 3 \right)\]
\[\Rightarrow 100={{2}^{2}}\times {{5}^{2}}..................\left( 4 \right)\]
Now let us substitute equation (3) and (4) in equation (2), we get
 \[\Rightarrow S=\dfrac{{{2}^{2}}\times 3\times 17}{{{2}^{2}}\times {{5}^{2}}}\]
Let us consider the above equation as equation (5).
\[\Rightarrow S=\dfrac{{{2}^{2}}\times 3\times 17}{{{2}^{2}}\times {{5}^{2}}}.........\left( 5 \right)\]
As we can observe \[{{2}^{2}}\]as common in numerator and denominator of equation of (5).
So, by simplifying the equation (5), we get
\[\Rightarrow S=\dfrac{51}{25}\]
Let us consider this equation as equation (6).
\[\Rightarrow S=\dfrac{51}{25}........\left( 6 \right)\]
Therefore by converting 2.04 as a fraction we get\[\dfrac{51}{25}\].

Note: We should note a point that if we want to convert a decimal number (>1) into a fraction, first we should count no of places that are there after the decimal and note them as ‘n’. Then we have to divide the decimal by \[{{10}^{n}}\]to eliminate the decimal and to convert it as a fraction.