Question

How do you write the numbers in order from least to greatest: \[ - \dfrac{{12}}{5}, - 1.35, - 1\dfrac{7}{9}\]?

Answer 1

Hint: Here, we will convert the given fractions into a decimal number. Then we will compare the numbers to each other to arrange the numbers from the least to the greatest number that is in ascending order. Ascending Order is a method of sorting the numbers from the lowest value to the highest value which is also in the increasing order.

Complete Step by Step Solution:
We are given with the integers \[ - \dfrac{{12}}{5}, - 1.35, - 1\dfrac{7}{9}\].
Now, we will convert the numbers in the form of fractions into integers.
\[ - \dfrac{{12}}{5} = - 2.4\]
Now, we will convert the mixed fraction into an improper fraction and then convert the improper fraction into a decimal number. So, we get
\[ - 1\dfrac{7}{9} = - \dfrac{{9\left( 1 \right) + 7}}{9}\]
Now, we will simplify the numerator in the fraction, we get
\[ \Rightarrow - 1\dfrac{7}{9} = - \dfrac{{9 + 7}}{9} = - \dfrac{{16}}{9}\]
\[ \Rightarrow - 1\dfrac{7}{9} = - 1.77\]
Now, we get all the integers in the form of decimals as \[ - 2.4, - 1.77, - 1.35\]
\[ - 2.4\] is the Least Integer among the given Integers.
\[ - 1.77\] is greater than the Least Integer \[ - 2.4\].
\[ - 1.35\] is greater than the Least Integer \[ - 1.77\].
Thus, the Increasing Order of the decimals is \[ - 2.4 < - 1.77 < - 1.35\] .
Thus, the Increasing order of the given integers is \[ - \dfrac{{12}}{5} < - 1\dfrac{7}{9} < - 1.35\]

Therefore, the Increasing order of the given integers from the least to the greatest is \[ - \dfrac{{12}}{5} < - 1\dfrac{7}{9} < - 1.35\].

Note:
We should remember that the highest number with a minus sign is the smallest value in the case of a negative integer. We can also arrange the numbers based on the number line. When we consider the integers from the right of zero in a number line, then it is said to be in Ascending order and when we consider the integers from the left of zero in a number line, then it is said to be in Descending Order. We should remember that the integer \[0\]lies between the negative integer and the positive integer.