ORDERING FRACTIONS AND DECIMALS

The following steps would be useful to order decimals from least to greatest.

Step 1 : 

Convert all the decimal numbers into fractions using multiplication of 10 or 100 or 1000 etc.,

Step 2 : 

Convert all  the fractions into like fractions (Having same denominator). 

Step 3 : 

Now, compare the numerators of the like fractions and order them from least to greatest or from greatest to least. 

Step 4 : 

Now, substitute the corresponding original values for fractions. 

Note : 

When you convert the decimal numbers into fractions, if there is only one digit after the decimal point, multiply and divide the decimal number by 10. 

If there are two digits after the decimal point, we have to multiply the decimal number by 100.   

Order set of values from least to greatest : 

Example 1 : 

17/24, 5/12, 9/16

Solution : 

Convert all the fractions into like fractions.  

We can use LCM method to make the denominators of the fractions same. 

Here, the denominators are 24, 12 and 16.

LCM of (24, 12, 16) = 48

Now, make the denominators of all the fractions as 48 using multiplication. 

17/24 = (17 ⋅ 2)/(24 ⋅ 2) = 34/48

5/12 = (5 ⋅ 4)/(12 ⋅ 4) = 20/48

9/16 = (9 ⋅ 3)/(16 ⋅ 3) = 27/48

Now, compare the numerators of like fractions above and order them from least to greatest.

20/48, 27/48, 34/48

Substitute the corresponding original fractions.  

5/12, 9/16, 17/24

Therefore, the order of the given fractions from least to greatest is 

5/12, 9/16, 17/24

Example 2 :

3/4, 2/5, 0.125

Solution : 

Convert the decimal number 0.125 into a fraction. 

0.125 = (0.125 ⋅ 1000)/1000  

0.125 = 125/1000

0.125 = 1/8

Substitute 1/8 for 0.125 in the given list of values.

Then, we have

3/4, 2/5, 1/8

Convert all the fractions in step 2 to like fractions.  

We can use LCM method to make the denominators of the fractions same. 

Here, the denominators are 4, 5 and 8.

LCM of (4, 5, 8) = 40

Now, make the denominators of all the fractions as 40 using multiplication. 

3/4 = (3 ⋅ 10)/(4 ⋅ 10) = 30/40

2/5 = (2 ⋅ 8)/(5 ⋅ 8) = 16/40

0.125 = 1/8 = (1 ⋅ 5)/(8 ⋅ 5) = 5/40

Now, compare the numerators of like fractions above and order them from least to greatest.

5/40, 16/40, 30/40

Substitute the corresponding original values.  

0.125, 2/5, 3/4

Therefore, the order of the given values from least to greatest is 

0.125, 2/5, 3/4

Example 3 :

5/6, 0.375, 1/4

Solution : 

Convert the decimal number 0.375 into a fraction. 

0.375 = (0.375 ⋅ 1000)/1000

0.375 = 375/1000

0.375 = 3/8

Substitute 3/8 for 0.375 in the given list of values.

5/6, 3/8, 1/4

Convert all the fractions to like fractions.  

We can use LCM method to make the denominators of the fractions same. 

Here, the denominators are 6, 8 and 4.

LCM of (6, 8, 4) = 24

Now, make the denominators of all the fractions as 24 using multiplication. 

5/6 = (5 ⋅ 4)/(6 ⋅ 4) = 20/24

0.375 = 3/8 = (3 ⋅ 3)/(8 ⋅ 3) = 9/24

1/4 = (1 ⋅ 6)/(4 ⋅ 6) = 6/24

Now, compare the numerators of like fractions above and order them from least to greatest.

6/24, 9/24, 20/24

Substitute the corresponding original values.  

1/4, 0.375, 5/6

Therefore, the order of the given values from least to greatest is 

1/4, 0.375, 5/6

Example 4 : 

1/20, 0.2, 0.074

Solution : 

Convert all the decimal numbers 0.2 and 0.074 into fractions. 

0.2 = (0.2 ⋅ 10)/10 = 2/10 = 1/5

0.074 = (0.074 ⋅ 1000)/1000 = 74/1000 = 37/500

Substitute 1/5 for 0.2 and 37/500 for 0.74 in the given list of values.

1/20, 1/5, 37/500

Convert all the fractions above to like fractions. 

We can use LCM method to make the denominators of the fractions same. 

Here, the denominators are 20, 5 and 500.

LCM of (20, 5, 500) = 500

Now, make the denominators of all the fractions as 500 using multiplication. 

1/20 = (1 ⋅ 25)/(20 ⋅ 25) = 25/500

0.2 = 1/5 = (1 ⋅ 100)/(5 ⋅ 100) = 100/500

0.074 = 37/500 = (37 ⋅ 1)/(500 ⋅ 1) = 37/500

Now, compare the numerators of like fractions above and order them from greatest to least.

100/500, 37/500, 25/500

Substitute the corresponding decimals.  

0.2, 0.074, 1/20

Therefore, the order of the given decimal numbers from least to greatest is 

0.2, 0.074, 1/20

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