ORDERING FRACTIONS AND DECIMALS FROM LEAST TO GREATEST

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

Problem 9 :

Write these numbers in order of size. Start with the smallest number.

60%, 1/2, 0.3, 3.4, 0.4

Solution :

60% can be written by writing the denominator as 100.

60% = 60/100

To convert it into decimal, since we have two zeroes in 100, we have to move the decimal two digits to the left.

1/2 = 0.5

0.3, 3.4, 0.4

These are already decimals, so the comparision can be made simply now.

0.3, 0.4, 0.5, 0.6, 3.4

Arranging 

0.3, 0.4, 1/2, 60%, 3.4

Problem 10 :

The heights of seven footballers are listed below.

1.9 m, 1.82 m, 1.78 m, 1.8 m, 1.88 m, 1.86 m, 1.7 m

(a) Arrange the heights in order from smallest to largest.

(b) Write down the median height.

(c) A player is picked at random. Write down the probability that he is over 1.85 m.

Solution :

(a) Arrange the heights in order from smallest to largest.

Given that,

1.9 m, 1.82 m, 1.78 m, 1.8 m, 1.88 m, 1.86 m, 1.7 m

Arranging from smallest to largest,

1.7, 1.78, 1.8, 1.82, 1.86, 1.88, 1.9

(b) Median height = 1.82

(c) Total number of samples = 7

Number of samples which are more than 1.85 = 3

Required probability = 3/7

Problem 11 :

Astronaut A is making some food. He needs to add 1 litres of water to the powder. Astronaut B is preparing a different meal. She needs to add 1.2 litres of water. How many more millilitres of water does astronaut A’s food need compared with astronaut B’s?

Solution :

Amount of water Astronaut A needs to add = 1 liter

Amount of water Astronaut B needs to add = 1.2 liter

Astronaut B wants to add more quantity of water, to find how much more we have to find the difference.

= 1.2 - 1

= 0.2 liters.