HOW TO CONVERT DECIMALS TO FRACTIONS

Write as a Fraction in Simplest Form :

Problem 1 :

0.3

Solution :

We consider the denominator as 1.

= (0.3)/1

Here the 3 is the tenth place after the decimal point.

So, we have to multiply the numerator and denominator by 10.

= [(0.3)/1) × (10/10)]

= 3/10

Problem 2 :

0.9

Solution :

We consider the denominator as 1.

= 0.9/1

Multiply both numerator and denominator by 10.

= [(0.9)/1) × (10/10)]

= 9/10

Problem 3 :

1.2

Solution :

We consider the denominator as 1.

= 1.2/1

Multiply both numerator and denominator by 10.

= [(1.2)/1) × (10/10)]

= 12/10

= 6/5

Converting the improper fraction to mixed fraction, we get

= 1  1/5

Problem 4 :

2.5

Solution :

We consider the denominator as 1.

= 2.5/1

Multiply both numerator and denominator by 10.

= [(2.5)/1) × (10/10)]

= 25/10

= 5/2

Converting the improper fraction to mixed fraction, we get

= 2  1/2

Problem 5 :

0.02

Solution :

We consider the denominator as 1.

= 0.02/1

Multiply both numerator and denominator by 100.

= [(0.02/1) × (100/100)]

= 2/100

= 1/50

Problem 6 :

0.07

Solution :

We consider the denominator as 1.

= 0.07/1

Multiply both numerator and denominator by 100.

= [(0.07/1) × (100/100)]

= 7/100

Problem 7 :

0.04

Solution :

We consider the denominator as 1.

= 0.04/1

Multiply both numerator and denominator by 100.

= [(0.04/1) × (100/100)]

= 4/100

= 1/25

Problem 8 :

0.125

Solution :

We consider the denominator as 1.

= 0.125/1

Multiply both numerator and denominator by 1000.

= [(0.125/1) × (1000/1000)]

= 125/1000

= 25/200

= 1/8

Write as a Fraction in Simplest Form :

Problem 9 :

0.27

Solution :

We consider the denominator as 1.

= 0.27/1

Multiply both numerator and denominator by 100.

= [(0.27)/1) × (100/100)]

= 27/100

Problem 10 :

0.84

Solution :

We consider the denominator as 1.

= 0.84/1

Multiply both numerator and denominator by 100.

= [(0.84)/1) × (100/100)]

= 84/100

= 42/50

= 21/25

Problem 11 :

0.025

Solution :

We consider the denominator as 1.

= 0.025/1

Multiply both numerator and denominator by 1000.

= [(0.025)/1) × (1000/1000)]

= 25/1000

= 1/40

Problem 12 :

0.275

Solution :

We consider the denominator as 1.

= 0.275/1

Multiply both numerator and denominator by 1000.

= [(0.275)/1) × (1000/1000)]

= 275/1000

= 55/200

= 11/40

Problem 13 :

0.825

Solution :

We consider the denominator as 1.

= 0.825/1

Multiply both numerator and denominator by 1000.

= [(0.825)/1) × (1000/1000)]

= 825/1000

= 165/200

= 33/40

Problem 14 :

0.00005

Solution :

We consider the denominator as 1.

= 0.00005/1

Multiply both numerator and denominator by 100000.

= [(0.00005)/1) × (100000/100000)]

= 5/100000

=1/20000

Problem 15 :

4.08

Solution :

We consider the denominator as 1.

= 4.08/1

Multiply both numerator and denominator by 100.

= [(4.08)/1) × (100/100)]

= 408/100

= 204/50

= 102/25

Converting the improper fraction to mixed fraction, we get

= 4  2/25

Problem 16 :

Two protected bird species in Florida are the whooping crane and the piping plover. How many times greater is the weight of a whooping crane than the weight of the piping plover? Write each weight as a mixed number.

Solution :

Weight of Whooping crane = 246.25 ounces

Converting into fractions, we get

= 24625/100

= 985 / 4 ounces

Weight of Piping Plover = 1  7/8 ounces

Converting into improper fraction, we get

= 15/8 ounces

Number of times that Wooping crane is greater than Piping plover 

= 985/4 ÷ 15/8

= 985/4 ⋅ 8/15

= (197 ⋅ 2)/3

= 394/3

= 131  1/3 ounces

Problem 17 :

Find a decimal with a value between 0.25 and 0.5. Write both the decimal and the equivalent fraction.

Solution :

Given decimals are, 0.25 and 0.5

Converting into fraction, we get

= 25/100 and 50/100

Fractions which lie between these two are,

26/100, 27/100, 28/100, 29/100, 30/100, ..............

Converting into decimal, we get

= 0.26, 0.27, 0.28, 0.29, 0.30, ............

Problem 18 :

Describe and correct the error in writing 0.073 as a fraction.

Solution :

Given decimal is 0.073

Number of digits after the decimal is 3, so we have to multiply both numerator and denominator by 1000.

= 0.073 ⋅ (1000/1000)

= 73/1000

The error is the denominator should be 1000. It is shown 100.

Problem 19 :

The thickness of a cell phone is 0.46 inch. Write the thickness as a fraction in simplest form.

Solution :

Thickness of cell phone = 0.46 inch

Converting into fraction, we get

= 0.46 ⋅ (100/100)

= 46/100

Simplifying, we get

= 23/50

Problem 20 :

A movie is 2.3 hours long. Write the length of the movie as a mixed number in simplest form.

Solution :

Duration time of movie = 2.3 hours

Converting into fraction, we get

= 23/10

Here after it cannot be simplified.

Problem 21 :

A person runs 26.22 miles in a marathon. Write the number of miles as a mixed number in simplest form.

Solution :

Distance covered in a marathon = 26.22

Converting into fraction, we get

= 2622/100

= 1311/10 miles