Question

Order the decimal expressions from greatest to least: $0.5$ , $0.75$and $0.55$.

Answer 1

The given question requires us to arrange the given decimal expressions in descending order. Hence, we have to arrange the decimal expression of greatest value first followed by smaller decimal expressions. We can also compare decimal expressions directly and by converting them into fractions.

Complete step by step Answer:
For comparing the decimal expressions and arranging them from greatest to least, we convert the given decimal expressions in fraction form.

Converting all the decimal expressions to fractions, we get,
$0.5 = \dfrac{5}{{10}}$, $0.75 = \dfrac{{75}}{{100}}$ and $0.55 = \dfrac{{55}}{{100}}$ .

In order to arrange the fractions from greatest to least, we need to have same denominator of these fractions,

L.C.M. of $10$, $100$ and $100$ is $100$.

So, Making the denominators of all the fractions equal to $100$ so as to compare their values.

So, $0.5 = \dfrac{5}{{10}} = \dfrac{{50}}{{100}}$, $0.75 = \dfrac{{75}}{{100}}$ and $0.55 = \dfrac{{55}}{{100}}$ .

Now, the terms of denominator of all the fractions are equal or same, so we compare the terms in numerators.

On comparing the numerators, we get,
$75 > 55 > 50$

So, $\dfrac{{75}}{{100}} > \dfrac{{55}}{{100}} > \dfrac{{50}}{{100}}$

Therefore, $0.75 > 0.55 > 0.5$

So, the order of the decimal expressions $0.5$, $0.75$ and $0.55$ from greatest to least is $0.75 > 0.55 > 0.5$.

Note: The given question deals with arranging the given decimal expressions from greatest to lowest.

The problem can be solved by various methods. We can also directly compare the decimal expressions by the face value of the digits at different place values.

Among the given decimal expressions in the question, $0.75$ has $7$ at tenths place, $0.55$ has $5$at tenths place and $0.5$ has $5$ at tenths place. Similarly, we can do further for hundredths place value. So, we can directly conclude that $0.75 > 0.55 > 0.5$.