Question

How do you write \[ - 1\dfrac{4}{5}\] as a decimal number?

Answer 1

Hint: For solving the question, we should have some knowledge of multiplication, addition and division as we will be requiring these things in these problems. First, convert the proper fraction into an improper fraction. After that divide the numerator by denominator to get the required decimal number.

Complete step-by-step answer:
We have to convert the given fraction into a decimal number. This can be done by converting the mixed fraction to the improper fraction and then converting the improper fraction to a decimal number.
Given fraction is\[ - 1\dfrac{4}{5}\],
Now convert the given fraction to an improper fraction, by converting the numerator will become,
\[ \Rightarrow - 1 \times 5 + 4\],
Now multiply the terms as multiplication should be done first and then add,
\[ \Rightarrow - 5 + 4 = - 1\],
Now the fraction will be equal to,
\[ \Rightarrow \dfrac{{ - 1}}{5}\],
Now by dividing the numerator by denominator, we get,
$ \Rightarrow 5\mathop{\left){\vphantom{1\begin{gathered}
   - 10 \\
  \dfrac{{ - 10}}{0} \\
\end{gathered} }}\right.
\!\!\!\!\overline{\,\,\,\vphantom 1{\begin{gathered}
   - 10 \\
  \dfrac{{ - 10}}{0} \\
\end{gathered} }}}
\limits^{\displaystyle \,\,\, { - 0.2}}$,
So remainder is -0.2, when we divide -1 by 5,
\[ \Rightarrow \dfrac{{ - 1}}{5} = - 0.2\],
The decimal number will be equal to\[ - 0.2\].

\[\therefore \]The required decimal number for the given fraction\[ - 1\dfrac{4}{5}\] will be equal to\[ - 0.2\].

Note:
Fractions and decimals are similar because they both in a way express partial numbers. Just as a decimal can be expressed as a fraction, it can be another way round as well. A fraction can also be converted into a decimal by simply dividing the numerator with the denominator. Also fractions can be expressed as decimals by simply performing the division of the ratio. We can also express decimals as fractions in terms of tenths, hundredths, thousandths, and so on.