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

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Last updated date: 23rd Feb 2024
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IVSAT 2024
Answer
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Hint: An improper fraction is a fraction whose numerator is greater than its denominator. For example, $\dfrac{5}{4}$. A mixed fraction is a fraction of the form $c\dfrac{n}{d}$, where cc is an integer and $n{\text{ < }}d$. For example, $\dfrac{{11}}{4} = 2\dfrac{3}{4}$. It is therefore the sum of a whole number and a proper fraction.Terminating decimals: these have a finite number of digits after the decimal point. Recurring decimals: these have one or more repeating numbers or sequences of numbers after the decimal point, which continue infinitely. These numbers are called irrational numbers and cannot be expressed as a fraction.

Complete step by step answer:
When we have a denominator in a fraction, which is in its smallest form and has as its factors prime numbers other than 2 and 5, you cannot write the fraction as a terminating decimal .
$ \Rightarrow - 1\dfrac{4}{5}$
$ \Rightarrow - (1 + \dfrac{4}{5})$
$ \Rightarrow - (\dfrac{5}{5} + \dfrac{4}{5})$
$ \Rightarrow - \dfrac{9}{5}$
In this case, we get terminating decimal
Dividing 9 by 5 using division, we get
$ \Rightarrow - 1.8$
$\therefore - \dfrac{9}{5} = - 1.8$ And $ - 1\dfrac{4}{5} = - 1.8$

Note: An improper fraction, with the name, signifies that the fractions are not done in a proper manner for any number, object or any element. In terms of Maths, an improper fraction has a numerator bigger than the denominator whereas in a proper fraction the denominator is greater than the numerator. Fractions have two parts, numerator and denominator. For example, in $\dfrac{1}{3}$ fraction, 1 is the numerator and 3 is the denominator.
Fractions usually show, if any number or object is parted into a number of parts, which in combination gives a value of 1.
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