**Converting Between Percents Decimals and Fractions :**

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

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

**Proper fraction to decimal**

**Improper fraction to decimal**

**Mixed fraction to decimal**

**Proper fraction to percentage**

**Improper fraction to percentage**

**Decimal to percentage**

**Decimal to fraction**

**Percentage to fraction**

**Percentage to decimal**

**Problem 1 :**

Convert the percentage given below into a proper fraction

2.4%

**Solution :**

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

Hence the proper fraction equal to the given percentage is 3/125

**Problem 2 :**

Convert the percentage given below into a proper fraction

0.55%

**Solution :**

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

Hence the proper fraction equal to the given percentage is 11/2000.

**Problem 3 :**

Convert the percentage given below into a proper fraction

0.25%

**Solution :**

0.25% = 0.25/100 = 25/10000

Hence the proper fraction equal to the given percentage is 1/400.

**Problem 4 :**

Convert the percentage given below into an improper fraction

125%

**Solution :**

125% = 125/100 = 5/4

Hence the improper fraction equal to the given percentage is 5/4

**Problem 5 :**

Convert the percentage given below into an proper fraction

15%

**Solution :**

15% = 15/100 = 3/20

Hence the improper fraction equal to the given percentage is 3/20

**Problem 6 :**

Convert the given fraction into decimal

3/20

**Solution : **

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

So, we have

3/20 = (3 ⋅ 5) / (20 ⋅ 5) = 15 / 100 = 0.15

Hence, 3/20 = 0.15

**Problem 7 :**

Covert the given fraction into decimal

7/10

**Solution : **

In the fraction, the denominator is 10.

So, we have

7/10 = 0.7

Hence, 7/10 = 0.7

**Problem 8 :**

Covert the fraction into decimal

3/50

**Solution : **

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

So, we have

3/50 = (3 ⋅ 2) / (50 ⋅ 2) = 6/100 = 0.06

Hence, 3/50 = 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.

So, we have

1/2 = (1 ⋅ 5) / (2 ⋅ 5) = 5/10 = 0.5

Hence, 1/2 = 0.5

**Problem 10 :**

Covert the fraction into decimal

3/4

**Solution : **

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

So, we have

3/4 = (3 ⋅ 25) / (4 ⋅ 25) = 75/100 = 0.75

Hence, 3/4 = 0.75

**Problem 11 : **

Convert the fraction into 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 ⋅ 100 % = 66.66%

Hence, 2/3 = 66.66 %

**Problem 12 : **

Convert the given fraction into 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 ⋅ 100 % = 83.33%

Hence, 5/6 = 83.33%

**Problem 13 : **

Convert the given fraction into 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 ⋅ 100 % = 41.66%

Hence, 5/12 = 41.66 %

**Problem 14 : **

Convert the given fraction into 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 ⋅ 100 % = 562.5 %

Hence, 45/8 = 562.5 %

**Problem 15 : **

Convert the given fraction into 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 ⋅ 100 % = 333.33 %

Hence, 10/3 = 333.33 %

After having gone through the stuff given above, we hope that the students would have understood "Converting between percents decimals and fractions".

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