Question

How do you order the following from the least to greatest without a calculator \[\] $ - \sqrt {10} , - \dfrac{{10}}{3}, - 3, - 2.95, - 3\dfrac{1}{4}, - 3.5 \times {10^0} $ ?

Answer 1

Hint: Numbers can be ordered in two ways – ascending and descending. Ascending is arranging from least to greatest number. We can order the numbers in ascending order only when they are of the same form. In order to solve this question, we need to convert the terms into the same form.

Complete step by step solution:
We are given,
 $ - \sqrt {10} , - \dfrac{{10}}{3}, - 3, - 2.95, - 3\dfrac{1}{4}, - 3.5 \times {10^0} $
It can also be written as,
 $ \Rightarrow - \sqrt {10} , - \dfrac{{10}}{3}, - 3, - 2.95, - 3\dfrac{1}{4}, - 3.5 $
Now, we’ll convert the terms into similar form
 $ \Rightarrow - \sqrt {10} = - 3.16 $
 $ \Rightarrow - \dfrac{{10}}{3} = - 3.33 $
 $ \Rightarrow - 3\dfrac{1}{4} = - 3.25 $
 $ \Rightarrow - 3.16, - 3.33, - 3, - 2.95, - 3.25, - 3.5 $
 $ \Rightarrow - 3.5, - 3.33, - 3.25, - 3.16, - 3, - 2.95, $
This is the required order.
So, the correct answer is “ $ - 3.5, - 3.33, - 3.25, - 3.16, - 3, - 2.95, $ ”.

Note: While arranging terms in ascending order we have to be extra cautious while arranging negative terms. When the terms are negative, larger the number, smaller the value of the term. Also, according to the laws of exponents anything to the power zero becomes $ 1 $ . Hence, $ {10^0} $ becomes $ 1 $ in the above solution.