Question

How do you change $-\dfrac{4}{5}$ into a decimal?

Answer 1

Hint: We are given a factor as $-\dfrac{4}{5}$ , we are asked to find the decimal expression for it. We will learn how we convert the fraction into decimal then we work on some examples. For our problem we multiply numerator and denominator by ‘2’ making the numerator as multiple of 10, then once we get it we will put decimal after 1 term from the right.

Complete step-by-step answer:
We are given a fraction as $-\dfrac{4}{5}$ , we are asked to change the term into decimal.
To do so we will first know how to change the fraction into decimal.
Now,
To change the terms into decimal we will first make their denominator as multiple of 10 then we will divide the term with that. We do this as this will make calculation little easy and error free.
Because when we divide the term by 10 or 100 or 1000, we do not need to divide it in actual, we just put the decimal after one digit of 2 digit from the right depending upon how many zero it has that is we divide by 10 then we place decimal after 1 term, if we divide by 100 it has 2 zero so we put decimal after 2 place.
For example, say we have $\dfrac{1}{2}$
So, we first make denominator a multiple of 10, denominator has just 2, we multiply it with 5.
The equation needs to keep the same so we multiply and divide the given fraction by 5.
So, $\dfrac{1}{2}=\dfrac{1}{2}\times \dfrac{5}{5}$
Solving we get –
$=\dfrac{5}{10}$
Now, as the denominator is 10, only one zero so decimal is put after 1 term.
So we get –
$=0.5$
Hence $\dfrac{1}{2}=0.5$
Now as like this we work on our problem we have $-\dfrac{4}{5}$ , denominator is 5, so we multiply it by 2 to make it as 10,
To balance the term we multiply numerator and denominator by 2.
So, we get –
$-\dfrac{4}{5}=-\dfrac{4}{5}\times \dfrac{2}{2}$
By simplifying, we get –
$=\dfrac{-8}{10}$
As it has 10 in the denominator, only 1 zero.
So, we put decimal after 1 place so, we get –
$=-0.8$
Hence, $-\dfrac{4}{5}=\dfrac{-8}{10}=-0.8$

Note: Another way to solve is to divide the term directly using long division, but this way the calculations in many problems will be little heavy and chances of error will be more.
Now by division directly, we divide 4 by 5
$\begin{align}
  & \left. {\underline {\,
 5 \,}}\! \right| 40\left| \!{\underline {\,
  0.8 \,}} \right. \\
 & \text{ 40} \\
 & \text{ X} \\
\end{align}$
So, $\dfrac{4}{5}=0.8$
Hence, $-\dfrac{4}{5}=-0.8$