Question

Write the following integers in decreasing order:
A) -15, 0, -2, -9, 7, 6, -5, 8.
B) -154, 123, -205, -89, -74

Answer 1

Hint: We will be using the concepts of the number system to solve the problem. We will also be using the concept of increasing order and decreasing order to sort the number given to us in the decreasing order. We will use the fact that negative numbers are less than the positive numbers and in negative numbers also the number which is greater in magnitude is less than the smaller one.

Complete step-by-step answer:
A) Now using definition, we have to arrange the numbers -15, 0, -2, -9, 7, 6, -5, 8 in decreasing order.
Now, we know that negative integers are always less than that of non- negative integers. So, we will first arrange them in decreasing order.
Now, we know that in negative numbers the number which is larger in magnitude is smaller. For example: \[ - 3 < - 2\].
Now, we have negative numbers as -15, -2, -9, -5. So, these numbers in decreasing will be,
$ \Rightarrow - 2 > - 5 > - 9 > - 15$
Now, we will arrange the non-negative integers in decreasing order. So, the non-negative integers are 0, 7, 6, 8.
Now, we will arrange them in decreasing order by seeing which number is less than others which we can do by differentiating numbers on the basis of digits and if the number has the same digits then we can compare the digit of the number from the left side. So, by doing this we have,
$ \Rightarrow 8 > 7 > 6 > 0$
Now, we have the numbers in decreasing orders as,
$\therefore 8 > 7 > 6 > 0 > - 2 > - 5 > - 9 > - 15$
Hence, the numbers in decreasing order are $8,7,6,0, - 2, - 5, - 9, - 15$.
B) Now using definition, we have to arrange the numbers -154, 123, -205, -89, -74 in decreasing order.
Now, we know that negative integers are always less than that of non- negative integers. So, we will first arrange them in decreasing order.
Now, we know that in negative numbers the number which is larger in magnitude is smaller. For example: \[ - 3 < - 2\].
Now, we have negative numbers as -154, -205, -89, -74. So, these numbers in decreasing will be,
$ \Rightarrow - 74 > - 89 > - 154 > - 205$
Now, there is only one non-negative number 123.
So, we have the numbers in decreasing orders as,
$\therefore 123 > - 74 > - 89 > - 154 > - 205$
Hence, the numbers in decreasing order are $123, - 74, - 89, - 154, - 205$.

Note: Increasing order: Numbers are said to be in increasing order when they are arranged from the smallest to the largest number.
Decreasing order: Numbers are said to be in decreasing order when they are arranged from the largest to the smallest number.