Question

How do you write $1\dfrac{3}{8}$ as a decimal?

Answer 1

Hint: First, we have to convert the given mixed fraction number to a fractional number. Thereafter, it is always better to look at the denominator first when we need to convert a fraction into decimal. If the denominator only has $2$ and $5$ as prime factors, one can easily select a number which when multiplied to the denominator converts the denominator, in a power of 10 and the result will be a limiting decimal.

Complete step-by-step answer:
First, we will convert $1\dfrac{3}{8}$ to a fractional number.
To do so, we need to know the steps which is,
Multiply the denominator (lower number) by the whole number and add the numerator (top number) and place it as the numerator of the new fractional number and the denominator remains as it is in the new fractional number.
Therefore,
$ \Rightarrow 1\dfrac{3}{8} = \dfrac{{(1 \times 8) + 3}}{8} = \dfrac{{11}}{8}$
So, now we need to turn $\dfrac{{11}}{8}$ into decimal.
As the only prime factor of the denominator which is $8$ is $2$.
 In fact there are three twos ($2 \times 2 \times 2$) , i.e., $(8) = 2 \times 2 \times 2$.
Further, we can convert the fraction $\dfrac{{11}}{8}$ by multiplying numerator and denominator by $5 \times 5 \times 5$ into $1000$, which is a power of $10$.
 Hence, $\dfrac{{11}}{8} = \dfrac{{11 \times 5 \times 5 \times 5}}{{8 \times 5 \times 5 \times 5}} = \dfrac{{1375}}{{1000}} = 1.375$
Therefore, we get that $\dfrac{{11}}{8}$ can be written as $1.375$ in decimal form.

Note: To turn a fraction to a decimal we need to know some rules. The fraction given must be an improper or a proper fraction and not a mixed fractional number. Decimal notation is a way of writing fractions which have their denominators in the powers of $10$. If the denominator of the given fraction only has $2$ and $5$ as prime factors, one can easily select a number which when multiplied to the denominator converts the denominator, in a power of 10 and the result will be a limiting decimal.