Question

How to order $\dfrac{1}{3},0.3,25\% ,\dfrac{2}{5}$ in ascending order?

Answer 1

Hint: We will first convert the percentage into the fraction and then write all the numbers in fraction form and then we will find the least common multiple and thus find the greatest number and accordingly.

Complete step-by-step answer:
We are given that we need to order $\dfrac{1}{3},0.3,25\% ,\dfrac{2}{5}$ in ascending order.
Here, the second number given is 0.3, we can write it as $\dfrac{3}{{10}}$.
Now, we have the third number as 25%.
We will divide it by 100 to find it in number form. So, the number will be $\dfrac{{25}}{{100}}$ that is equal to $\dfrac{1}{4}$.
Now, we have our numbers as $\dfrac{1}{3},\dfrac{3}{{10}},\dfrac{1}{4},\dfrac{2}{5}$ whom we need to arrange in ascending order.
Now, we will write all the numbers in the form so that they all have the same denominators.
So, we can write $\dfrac{1}{3}$ as $\dfrac{1}{3} \times \dfrac{{20}}{{20}} = \dfrac{{20}}{{60}}$.
Now, going on like this only, we have $\dfrac{3}{{10}}$ as $\dfrac{3}{{10}} \times \dfrac{6}{6} = \dfrac{{18}}{{60}}$, $\dfrac{1}{4}$ as $\dfrac{1}{4} \times \dfrac{{15}}{{15}} = \dfrac{{15}}{{60}}$ and $\dfrac{2}{5}$ as $\dfrac{2}{5} \times \dfrac{{12}}{{12}} = \dfrac{{24}}{{60}}$.
Now, we have the numbers $\dfrac{{20}}{{60}},\dfrac{{18}}{{60}},\dfrac{{15}}{{60}},\dfrac{{24}}{{60}}$.
Now, we can clearly compare them using their numerators.
Since 15 < 18 < 20 < 24.
So, we have $\dfrac{{15}}{{60}} < \dfrac{{18}}{{60}} < \dfrac{{20}}{{60}} < \dfrac{{24}}{{60}}$.
Hence, we have $\dfrac{1}{4} < \dfrac{3}{{10}} < \dfrac{1}{3} < \dfrac{2}{5}$.

Thus, we get $25\% < 0.3 < \dfrac{1}{3} < \dfrac{2}{5}$.

Note:
The students must note that the conversion we did, we use the fact that the least common multiple of the denominators of the fractions we have is 60.
Now, we also have an alternate way to do the same. Let us understand that as follows:-
We will convert all the numbers which are not in percentage form in percent and then compare them.
We are given that we need to order $\dfrac{1}{3},0.3,25\% ,\dfrac{2}{5}$ in ascending order.
Here, the first number given is $\dfrac{1}{3}$.
To convert it into percentage, we multiply it by 100 to obtain: $\dfrac{1}{3} \times 100 = 33.\overline 3 \% $.
Now, we have the second number as 0.3.
To convert it into percentage, we multiply it by 100 to obtain: $0.3 \times 100 = 30\% $.
Now we have the fourth number as $\dfrac{2}{5}$.
To convert it into percentage, we multiply it by 100 to obtain: $\dfrac{2}{5} \times 100 = 40\% $.
Now, we have the numbers \[33.\overline 3 \% ,30\% ,25\% ,40\% \].
Now, we can clearly compare them.
So, we get 25% < 30% < 30.333% < 40%.
Thus, we get $25\% < 0.3 < \dfrac{1}{3} < \dfrac{2}{5}$.