Question

How do you write these numbers in order from least to greatest: $ 0.65,2/3,3/5,0.5 $ ?

Answer 1

Hint: First we will start by either converting all the numbers that are fractions to decimals or the decimals to the fractions and then arrange them in the above mentioned order. Then finally arrange them in order.

Complete step by step solution:
We will first convert the numbers to one common form. We can convert all the fractions to decimal or all the decimals to one fraction.
Here, we will convert all the numbers to the decimal form. So, we start by converting $ 2/3 $
Now here we multiply the numerator and denominator by $ 100 $ and then reduce the terms until they cannot be reduced any further.
 \[\Rightarrow \dfrac{2}{3} = \left( {\dfrac{2}{3}} \right) \times \left( {\dfrac{{100}}{{100}}} \right) = \dfrac{{200}}{{300}} = 0.67\]
Now next we convert $ 3/5 $ into decimal.
Here also we multiply and divide by $ 2 $ and then reduce the term until they cannot be reduced any further.
 \[\Rightarrow \dfrac{3}{5} = \left( {\dfrac{3}{5}} \right) \times \left( {\dfrac{2}{2}} \right) = \dfrac{6}{{10}} = 0.6\]
Hence, all the converted numbers are: $ 0.65,\,0.50,\,0.60,\,0.67 $ .
Now, we arrange these terms according to ascending order.
 $\Rightarrow 0.5,\,0.6,\,0.65,\,0.67 $
These numbers can be arranged in their original form.
 $\Rightarrow 0.5,\,\,\dfrac{3}{5},\,\,0.65,\,\,\dfrac{2}{3} $ .
So, the correct answer is “ $ 0.5,\,\,\dfrac{3}{5},\,\,0.65,\,\,\dfrac{2}{3} $ ”.

Note: A fraction explains how many parts of a whole. It is expressed by a top number that is the numerator and a bottom number that is the denominator. A decimal is a fraction where the denominator is a power of ten such as $ 10,100,1000 $ , etc and can be written with a decimal point.
Always be sure that all of the terms are of the same type while comparing them. When you convert a fraction to a decimal make sure you back trace the same term to check if you have reduced the term correctly. While reducing terms make sure you reduce by making the factors.