Question

How do you write $12\dfrac{3}{{10}}$ as a decimal?

Answer 1

First change the mixed number into fractional number and then convert fractional number into decimal number.
In order to convert a mixed number $a\dfrac{b}{c}$ into fractional form you have to use the following formula
$a\dfrac{b}{c} = \dfrac{{a \times c + b}}{c}$

Complete step by step solution: To write the mixed number $12\dfrac{3}{{10}}$ in decimal numbers, we need to go through two steps,
Firstly we will convert the mixed number $12\dfrac{3}{{10}}$ into fraction number by following method
$a\dfrac{b}{c} = \dfrac{{a \times c + b}}{c}$
Let us convert the mixed number $12\dfrac{3}{{10}}$ into fraction number as following
$12\dfrac{3}{{10}} = \dfrac{{12 \times 10 + 3}}{{10}} = \dfrac{{120 + 3}}{{10}} = \dfrac{{123}}{{10}}$
Therefore the fractional form of mixed number $12\dfrac{3}{{10}}$ is $\dfrac{{123}}{{10}}$
Now we will convert the fraction number $\dfrac{{123}}{{10}}$ into decimal number,
In order to convert the fraction $\dfrac{{123}}{{10}}$ into decimal, we will do the long division
So dividing the numerator $123$ by denominator $10$ that is
$= 123 \div 10$
We can write it in long division method as
$= \left. {\overline {\, {10} \,}}\\! \right| \overline {123\;} \left| \\!{\overline {\, {} \,}} \right.$
Where the divisor is on the left side, dividend is in the middle and the quotient will be on the right side. Dividing
$123$ by $10$
$= \left. {\overline {\, {10} \,}}\\! \right| \overline {123\;} \left| \\!{\overline {\, 1 \,}} \right. \\\ \;\;\;\;\;\;\;\underline {10\;\;\;} \\\$
Subtracting $10$ from $12$ and writing the result below $10$ and also pulling $3$ down with the result

$$= \left. {\overline {\, {10} \,}}\\! \right| \overline {12\;3\;} \left| \\!{\overline {\, 1 \,}} \right. 2 \\\ \;\;\;\;\;\;\;\underline {10 \downarrow \;\;} \\\ \;\;\;\;\;\;\;\;2\;3 \\\ \;\;\;\; \\\$$

Again doing the same process with $23$

$$= \left. {\overline {\, {10} \,}}\\! \right| \overline {12\;3\;} \left| \\!{\overline {\, 1 \,}} \right. 2 \\\ \;\;\;\;\;\;\;\underline {10 \downarrow \;\;} \\\ \;\;\;\;\;\;\;\;2\;3 \\\ \;\;\;\;\;\;\;\;\underline {2\;0\;\;\;} \\\ \;\;\;\;\;\;\;\;\;\;3 \\\$$

We are getting $3$ as the remainder but we will not stop the division here, we will put a decimal in
quotient and divide it further until the remainder won’t equals $0$

$$= \left. {\overline {\, {10} \,}}\\! \right| \overline {12\;3\;} \left| \\!{\overline {\, {12.3} \,}} \right. \\\ \;\;\;\;\;\;\;\underline {10 \downarrow \;\;} \\\ \;\;\;\;\;\;\;\;2\;3 \\\ \;\;\;\;\;\;\;\;\underline {2\;0\;\;\;} \\\ \;\;\;\;\;\;\;\;\;\;3\;0 \\\ \;\;\;\;\;\;\;\;\;\;\underline {3\;0\;\;} \\\ \;\;\;\;\;\;\;\;\;\;0\;0 \\\$$

So finally we have got the remainder equals $0$
$\therefore$Quotient $= 12.3$ is the decimal form of the fraction $\dfrac{{123}}{{10}}$ and of the mixed form $12\dfrac{3}{{10}}$

Note: If remainder of a fraction is in powers of $10$ i.e. $10\;or\;100\;or\;1000\;etc..$ then we can directly convert them into decimal form by just putting a decimal $n$ digit after from the right side of the numerator. Where $n$ is the number of $0's$ the denominator has, try this method by yourself for this question.