Question

What is $2\dfrac{5}{8}$ as decimal form?

Answer 1

Hint: First of all convert the given mixed fraction into the improper fraction by using the conversion: $a\dfrac{b}{c}=\dfrac{ac+b}{c}$. Now, to convert this fraction into the decimal try to make the denominator equal to 10 or of the form ${{10}^{n}}$ where n will be any integer. For this, multiply the denominator with $5\times 5\times 5$ in the obtained improper fraction and to balance this change multiply the numerator also with the same. Write the denominator in the form ${{10}^{n}}$ and move the decimal point to the left side according to the number of zeroes in ${{10}^{n}}$.

Complete step by step solution:
Here we have been provided with a mixed fraction $2\dfrac{5}{8}$ and we are asked to convert it into the decimal form. But first we need to convert the mixed fraction into the improper fraction.
Now, if we have to convert any mixed fraction of the form $a\dfrac{b}{c}$ into an improper fraction then we use the conversion $a\dfrac{b}{c}=\dfrac{ac+b}{c}$. So we have,
\[\begin{align}
  & \Rightarrow 2\dfrac{5}{8}=\dfrac{\left( 2\times 8 \right)+5}{8} \\
 & \Rightarrow 2\dfrac{5}{8}=\dfrac{16+5}{8} \\
 & \Rightarrow 2\dfrac{5}{8}=\dfrac{21}{8} \\
\end{align}\]
Now, to convert this improper fraction into the decimal we need to make the denominator equal to 10 or of the form ${{10}^{n}}$ where n will be any integer. Clearly, we can see that we have 8 which can be written as $8=2\times 2\times 2$. So, to make the denominator of the form ${{10}^{n}}$ we need to multiply each 2 with 5 that means we have to multiply the denominator with $5\times 5\times 5$. To balance the expression we have to multiply the numerator also with the same number, so we get,
\[\begin{align}
  & \Rightarrow \dfrac{21}{8}=\dfrac{21\times 5\times 5\times 5}{2\times 2\times 2\times 5\times 5\times 5} \\
 & \Rightarrow \dfrac{21}{8}=\dfrac{2625}{{{\left( 2\times 5 \right)}^{3}}} \\
 & \Rightarrow \dfrac{21}{8}=\dfrac{2625}{{{10}^{3}}} \\
\end{align}\]
Since the exponent of 10 is 3 so we need to move the decimal point three digits to the left, so we get,
\[\Rightarrow \dfrac{21}{8}=2.625\]
Hence, the decimal form of $2\dfrac{5}{8}$ is 2.625.

Note: You may see that the above obtained decimal number in terminating in nature. So you may take an important point from here that you can convert a fraction into the terminating decimal only if its denominator can be written in the form ${{10}^{n}}$. In all other cases the decimal will be non – terminating and repeating in case of rational numbers.