ORDERING FRACTIONS AND DECIMALS FROM LEAST TO GREATEST

To compare two quantities, they should be in the same kind.

Fraction with another fraction can be compared easily. Decimal with another decimal can be compared easily.

If we want to compare fraction and decimal, first let us check whether it is simple to make the fraction as decimal without performing long division.

If we have 10, 100, 1000, ....... at the denominator, we can simply change it as decimal.

Some times it will be very simple to convert fraction as decimal by making the denominator as multiple of 10's.

For example,

In the following exercises, write each set of numbers in order from least to greatest.

Problem 1 :

3/5, 9/16, 0.55

Solution :

Let us change 3/5 to a decimal.

(3/5) ∙ (20/20) = 60/100 = 0.6

Doing long division, we can convert 9/16 as decimal.

9/16 = 0.56

Compare the decimals

0.55 < 0.56 < 0.6

Substitute the corresponding original fraction

Least to greatest

0.55 < 9/16 < 3/5

Converting as 10's, 100's ....etc

To make it as multiple of 10.

4 x 25 = 100

8 x 125 = 1000

5 x 2 =10

To convert the decimal as fraction, we have to observe that the number of digits after the decimal.

If we have one digit after the decimal, we have to multiply it by (10/10)
If we have two digits after the decimal, we have to multiply it by (100/100)

In the following exercises, write each set of numbers in order from least to greatest.

Problem 2 :

3/8, 7/20, 0.36

Solution :

Doing long division, we can convert 3/8 as decimal.

3/8 = 0.375

(7/20)∙(5/5) = 35/100 ==> 0.35

Compare the decimals

0.35 < 0.36 < 0.375

Substitute the corresponding original fraction

Least to greatest

7/20 < 0.36 < 3/8

Problem 3 :

0.702, 13/20, 5/8

Solution :

Doing long division, we can convert 13/20 and 5/8 as decimal.

(13/20) ∙ (5/5) = 65/100 ==> 0.65

(5/8) ∙ (125/125) = 625/1000 ==> 0.625

Compare the decimals

0.625 < 0.65 < 0.702

Substitute the corresponding original fraction

Least to greatest

5/8 < 13/20 < 0.702

Problem 4 :

0.15, 3/16, 1/5

Solution :

Doing long division, we can convert 3/16 as decimal.

3/16 = 0.187

Let us change 1/5 to a decimal.

(1/5) ∙ (20/20) = 20/100 = 0.2

Compare the decimals

0.15 < 0.187 < 0.2

Substitute the corresponding original fraction

Least to greatest

0.15 < 3/16 < 1/5

Problem 5 :

-0.3, -1/3, -7/20

Solution :

Doing long division, we can convert -1/3as decimal.

-1/3 = -0.33

(-7/20) ∙ (5/5) = -35/100 ==> -0.35

Compare the decimals

-0.35 < -0.33 < -0.3

Substitute the corresponding original fraction

Least to greatest

-7/20 < -1/3 < -0.3

Problem 6 :

-0.2, -3/20, -1/6

Solution :

(-3/20) ∙ (5/5) = -15/100 ==> -0.15

Doing long division, we can convert -1/6 as decimal.

-1/6 = -0.16

Compare the decimals

-0.2 < -0.16 < -0.15

Substitute the corresponding original fraction

Least to greatest

-0.2 < -1/6 < -3/20

Problem 7 :

-3/4, -7/9, -0.7

Solution :

Let change -3/4 to a decimal

(-3/4) ∙ (25/25) = -75/100 = -0.75

Doing long division, we can convert -7/9 as decimal.

-7/9 = -0.778

Compare the decimals

-0.778 < -0.75 < -0.7

Substitute the corresponding original fraction

Least to greatest

-7/9 < -3/4 < -0.7

Problem 8 :

-8/9, -4/5, -0.9

Solution :

Doing long division, we can convert -8/9 as decimal.

-8/9 = -0.88

Let change -4/5 to a decimal

(-4/5) ∙ (20/20) = -80 /100 = -0.8

Compare the decimals

-0.9 < -0.88 < -0.8

Substitute the corresponding original fraction

Least to greatest

-0.9 < -8/9 < -4/5

ORDERING FRACTIONS AND DECIMALS FROM LEAST TO GREATEST

Converting as 10's, 100's ....etc

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