CONVERTING FRACTIONS TO DECIMALS

To convert fractions to decimal, first we have to look at the denominator of the fraction. 

In this topic, we may receive three types of questions.

Case 3 :

Using long division, we can convert fraction into decimal.

In the following exercises, convert each fraction to a decimal.

Problem 1:

2/5

Solution:

Let change 2/5 to a decimal

(2/5) ∙ (20/20) = (40/100) ==> 0.4

2/5 = 0.4

Problem 2:

4/5

Solution:

Let change 4/5 to a decimal

(4/5) ∙ (20/20) = (80/100) ==> 0.8

4/5 = 0.8

Problem 3:

-3/8

Solution:

Let change -3/8 to a decimal

(-3/8) ∙ (125/125) = (-375/1000) ==> -0.375

-3/8 = -0.375

Problem 4:

-5/8

Solution:

Let change -5/8 to a decimal

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

-5/8 = -0.625

Problem 5:

17/20

Solution:

Let change 17/20 to a decimal

(17/20) ∙ (5/5) = (85/100) ==> 0.85

17/20 = 0.85

Problem 6:

13/20

Solution:

Let change 13/20 to a decimal

(13/20) ∙ (5/5) = (65/100) ==> 0.65

13/20 = 0.65

Problem 7:

11/4

Solution:

Let change 11/4 to a decimal

(11/4) ∙ (25/25) = (275/100) ==> 2.75

11/4 = 2.75

Problem 8:

17/4

Solution:

Let change 17/4 to a decimal

(17/4) ∙ (25/25) = (425/100) ==> 4.25

17/4 = 4.25

Problem 9:

-310/25

Solution:

Let change -310/25 to a decimal

(-310/25) ∙ (4/4) = (1240/100) ==> 12.4

-310/25 = 12.4

Problem 10:

-284/25

Solution:

Let change -284/25 to a decimal

(-284/25) ∙ (4/4) = (1136/100) ==> 11.36

-284/25 = 11.36

Problem 11 :

5/9

Solution:

Doing long division, we can convert 5/9 as decimal.

5/9 = 0.55

Problem 12 :

2/9

Solution:

Doing long division, we can convert 2/9 as decimal.

2/9 = 0.22

Problem 13 :

You send 40 text messages in one month. The total cost is $4.80. How much does each text message cost?

Solution :

Number of text messages in one month = 40

Total cost = $4.80

Amount spent for each text message = 40/4.80

= (40/4.8) x (10/10)

= 400/48

= $8.33

So, cost of each text message is $8.33

Problem 14 :

Of the two bottles of sunblock shown, which is the better buy? Explain.

Solution :

So, cost of 5 ounce bottle is cheaper.

Problem 15 :

A supplier sells 2  1/4 pounds of mulch for every 1  1/3 pounds of gravel. The supplier sells 172 pounds of mulch and gravel combined. How many pounds of each item does the supplier sell?

Solution :

1  1/3 pound of gravel = 2  1/4 pound of mulch

1 pound of gravel = 2  1/4 / 1  1/3

= 9/4 / 4/3

= 9/4 x 3/4

= 27/16

Let x be the amount of gravel.

x + (27/16)x = 172

(16x + 27x)/16 = 172

43x / 16 = 172

43x = 172(16)

43x = 2752

x = 2752/43

x = 64

Amount of gravel = 64 pounds and amount of multch = (27/16) x

= (27/16) 64

= 108 pounds

Problem 16 :

After earning interest, the balance of an account is $420. The new balance is 7/6 of the original balance. How much interest did it earn?

Solution :

Original balance = $420

Amount of interest = 7/6 of original balance

= (7/6) x 420

= (7 x 420)/6

= 7 x 70

New balance = 490

Interest = Old balance - new balance

= 490 - 420

= $70

Problem 17 :

You clean a community park for 6.5 hours. You earn $42.25. How much do you earn per hour?

Solution :

Time taken = 6.5 hours

Amount he earns = $42.25

Amount he earns per hour = 42.25/6.5

= 6.5

So, the amount he earns per hour is $6.5

Problem 18 :

These are some of Brianʼs summer exam results.

Art  = 14/25

Biology = 64%

German = 49%

Latin = 25/43

Music = 11/15

Physics = 54%

Arrange the subjects in order, starting with the best result.

Solution :

By converting into decimals,

0.56, 0.64, 0.49, 0.58, 0.73, 0.54

0.49, 0.54, 0.56, 0.58, 0.64, 0.73

Arrnaging the subject from best to least,

German, Physics, Art, Latin, Biology, Physics