COMPARING FRACTIONS DECIMALS AND PERCENTAGES

Order this list from smallest to largest.

Problem 1 :

0.3, 15%, 2, 1/2

Solution :

15% = 15/100 = 0.15

1/2 = 0.5

0.3, 0.15, 2, 0.5

So, the number smallest to largest is 0.15 < 0.3 < 0.5 < 2.

Problem 2 :

3/4, 3, 0.4, 5%

Solution :

3/4 = 0.75

5% = 0.05

0.75, 3, 0.4, 0.05

So, the number smallest to largest is  0.05 < 0.4 < 0.75 < 3.

Problem 3 :

0.14, 4%, 0.48, 1/5

Solution :

4% = 0.04

1/5 = 0.2

0.14, 0.04, 0.48, 0.2

So, the number smallest to largest is 0.04 < 0.14 < 0.2 < 0.48.

Problem 4 :

0.46, 3%, 1/4, 0.14

Solution :

3% = 0.03

1/4 = 0.25

0.46, 0.03, 0.25, 0.14

So, the number smallest to largest is 0.03 < 0.14 < 0.25 < 0.46.

Problem 5 :

6/5, 58.9%, 1.77, 0.169

Solution :

6/5 = 1.2

58.9% = 0.589

1.2, 0.589, 1.77, 0.169

So, the number smallest to largest is 0.169 < 0.589 < 1.2 < 1.77.

Problem 6 :

The figure shows the portions of ultraviolet (UV) rays reflected by four different surfaces. How many times more UV rays are reflected by water than by sea foam?

Solution :

Measure of ultraviolet in sea form = 25%

= 25/100

= 0.25

Measure of ultraviolet in water = 21/25

Multiplying both numerator and denominator by 4, we get

= 21/25 x 4/4

= 84/100

= 0.84

Number of times more UV rays reflected by water than by sea form

= 0.84/0.25

= 3.36

So, water reflects about 3.4 times more UV rays than sea foam.

Problem 7 :

You, your sister, and a friend each take the same number of shots at a soccer goal. You make 72% of your shots, your sister makes 19/25 of her shots, and your friend makes 0.67 of his shots. Who made the fewest shots?

Solution :

Shots you make = 72%

Shots your sister make = 19/25

Shots your friend make = 0.67

To compare these three quantities, we have to make them into the same unit.

72% = 72/100

= 0.72

19/25 = (19/25) x (4/4)

= 76/100

= 0.76

0.67 is already is decimal.

Comparing 0.72, 0.76 and 0.67, arranging them from least to greatest.

0.67, 0.72, 0.76

0.67, 72%, 19/25

Your friend, you made, your sister

So, your friend made the fewest shots.

Problem 8 :

Students in a class were asked to tell their favorite color.

a. What percent said red, blue, or yellow?

b. How many times more students said red than yellow?

c. Use two methods to find the percent of students who said green. Which method do you prefer?

Solution :

a.

Percentage of red :

= 0.26

To convert the decimal into percentage, we have to multiply by 100%.

= 0.26 x 100%

= 26%

Percentage of blue :

= 40%

Percentage of yellow :

= 0.04

Multiplying by 100%, we get

= 0.04 x 100%

= 4%

b. Red than yellow = 0.26/0.04

= 6.5

c. The total percentage = 100%

Percentage of red + percentage of purple + percentage of green + percentage of yellow + percentage of blue = 100%

26% + 14% + percentage of green + 4% + 40% = 100%

(26 + 14 + 4 + 40)% + percentage of green = 100%

84% + percentage of green = 100%

Percentage of green = 100 - 84

= 16%

Problem 9 :

You make 75% of your shots, your sister makes 13/20 of her shots, and your friend makes 0.7 of his shots. Who made the most shots?

Solution :

Shots you make = 75%

Shots your sister make = 13/20

Shots your friend make = 0.7

To compare these three quantities, we have to make them into the same unit.

75% = 75/100

= 0.75

13/20 = (13/20) x (5/5)

= 65/100

= 0.65

0.65 is already is decimal.

0.7 is already decimal.

Comparing 0.75, 0.65, 0.7, arranging them from least to greatest.

0.65, 0.7, 0.75

13/20, 0.7, 75%

Your sister, you friend, your make

So, you made the most shots.

Problem 10 :

The map shows the portions of the U.S. population that live in five states. List the five states in order by population from least to greatest.

Solution :

Arranging from least to greatest :

2%, 3%, 4%, 6% 12%

Washington, Ohio, Michigan, New York, California