CONVERTING BETWEEN PERCENTS DECIMALS AND FRACTIONS

To solve many real world problems, we need to do conversions between percentages, decimals and fractions.

Let us see how to do conversions between percentages, decimals and fractions.

A half can be written as shown below.

A quarter can be written as shown below.

Conversions

Proper Fraction to Decimal :

7/25 = (7x4)/(25x4) = 28/100 = 0.28

Improper Fraction to Decimal :

17/5 = (17x2)/(5x2) = 34/10 = 3.4

Mixed Fraction to Decimal :

Proper Fraction to Percentage :

7/25 = (7x4)/(25x4) = 28/100 = 28%

Improper Fraction to Percentage :

17/5 = (17x20)/(5x20) = 340/100 = 340%

Decimal to Percentage :

2.742 = 2.742x100% = 274.2%

0.2742 = 0.2742x100% = 27.42%

0.0032 = 0.0032x100% = 0.32%

0.032 = 0.032x100% = 3.2%

0.32 = 0.32x100% = 32%

Decimal to Fraction :

0.32 = 32/100 = 8/25

1.25 = 125/100 = 5/4

Percentage to Fraction :

45% = 45/100 = 9/20

36.2% = 36.2/100 = 362/1000 = 181/500

Percentage to Decimal :

36% = 36/100 = 0.36

27.5% = 27.5/100 = 0.275

Solved Problems

Problem 1 :

Convert the percentage to a proper fraction.

2.4%

Solution :

2.4% = 2.4/100 = 24/1000 = 3/125

Problem 2 :

Convert the percentage to a proper fraction.

0.55%

Solution :

0.55% = 0.55/100 = 55/10000 = 11/2000

Problem 3 :

Convert the percentage to a proper fraction.

0.25%

Solution :

0.25% = 0.25/100 = 25/10000

Problem 4 :

Convert the percentage to an improper fraction.

125%

Solution :

125% = 125/100 = 5/4

Problem 5 :

Convert the percentage to a proper fraction.

15%

Solution :

15% = 15/100 = 3/20

Problem 6 :

Convert the fraction to decimal.

3/20

Solution :

In  the given fraction, the denominator is 20 which is convertible to 100 using multiplication by 5.

3/20 = (3x5)/(20x5) = 15/100 = 0.15

Problem 7 :

Covert the fraction into decimal.

7/10

Solution :

In  the fraction, the denominator is 10.

7/10 = 0.7

Problem 8 :

Covert the fraction to decimal.

3/50

Solution :

In the fraction number, the denominator is 50 which is convertible to 100 using multiplication by 2.

3/50 = (3x2)/(50x2) = 6/100 = 0.06

Problem 9 :

Covert the given fraction into decimal.

 1/2

Solution :

In the fraction, the denominator is 2 which is convertible to 10 using multiplication by 5.

1/2 = (1x5)/(2x5) = 5/10 = 0.5

Problem 10 :

Covert the fraction to decimal.

3/4

Solution :

In  the fraction, the denominator is 4 which is convertible to 100 using multiplication by 25.

3/4 = (3x25)/(4x25) = 75/100 = 0.75

Problem 11 :

Convert the fraction to percentage.

2/3

Solution :

Here, the denominator of the given fraction is 3 which can not be converted into 100 using multiplication.

So the given fraction can be converted into decimal using long division.

So, 2/3 = 0.6666 (approximately).

0.6666 = 0.6666 x 100% = 66.66%

Problem 12 :

Convert the fraction to percentage.

5/6

Solution :

Here, the denominator of the given fraction is 6 which can not be converted into 100 using multiplication.

So the given fraction can be converted into decimal using long division.

So, 5/6 = 0.8333 (approximately).

0.8333 = 0.8333 x 100% = 83.33%

Problem 13 :

Convert the fraction to percentage.

5/12

Solution :

Here, the denominator of the given fraction is 12 which can not be converted into 100 using multiplication.

So the given fraction can be converted into decimal using long division.

So, 5/12 = 0.4166 (approximately)

0.4166 = 0.4166 x 100% = 41.66%

Problem 14 :

Convert the fraction to percentage.

45/8

Solution :

Here, the denominator of the given fraction is 8 which can not be converted into 100 using multiplication.

So the given fraction can be converted into decimal using long division.

So, 45/8 = 5.625.

5.625 = 5.625 x 100% = 562.5 %

Problem 15 :

Convert the fraction to percentage.

10/3

Solution :

Here, the denominator of the given fraction is 3 which can not be converted into 100 using multiplication.

So the given fraction can be converted into decimal using long division.

So, 10/3 = 3.3333 (approximately).

3.3333 = 3.3333 x 100% = 333.33%

Problem 16 :

A student earned a grade of 80% on a math test that had 20 problems. How many problems on this test did the student answer correctly? (round to the nearest whole number)

Solution :

Total number of problems = 20

Percentage of problems he has earned = 80%

Number of problems he answered correctly 

= 80% of 20

= (80/100) x 20

= 80/5

= 18

He has answered 18 problems correctly. 

Problem 17 :

The percents of students who travel to school by car, bus, and bicycle are shown for a school of 825 students.

a. Write the percents as decimals.

b. Write the percents as fractions.

c. What percent of students use another method to travel to school?

Solution :

a.

Percentage of students who use car = 20%

= 20/100

= 0.20

Percentage of students who use bus = 48%

= 48/100

= 0.48

Percentage of students who use bicycle = 8%

= 8/100

= 0.08

b. 

Fraction of students who use car = 20/100

= 1/5

Percentage of students who use bus = 48/100

= 12/25

Percentage of students who use bicycle = 8/100

= 2/25

c. Percent of students use another method to travel to school

= 100 - (20 + 48 + 8)

= 100 - 76

= 24%

Kindly mail your feedback to v4formath@gmail.com

We always appreciate your feedback.