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Last updated on July 5th, 2025

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Decimals and Fractions

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A whole number and a fraction can be represented using the decimal number system. A fraction is written as a/b, and a decimal point (.) separates the whole number from the fraction. For example, 1.34 is a decimal number, and 1/5 is a fraction. We can easily convert a decimal number to a fraction and vice versa because they share a close relationship. To convert a decimal number into a fraction, first remove the decimal point, then write the number as a whole number divided by a power of 10. The power of 10 depends on the number of digits after the decimal point. Finally, simplify the fraction to its lowest terms. In this article, we will learn about the concepts and properties of decimals and fractions in detail.

Decimals and Fractions for UAE Students
Professor Greenline from BrightChamps

What is a Decimal Fraction?

A decimal fraction is a fraction where the denominator is a power of 10, such as 10, 100, or 1000. The bottom number of a fraction, known as the denominator, is a power of 10, such as 10, 100, 1000, and so on. In a decimal fraction, we write the fraction without the denominator by using a decimal point. Using decimals instead of fractions makes arithmetic operations like addition and multiplication easier. For example, 1/10 is a fraction, and we can write it as 0.1. Likewise, 4/100 can be written as 0.04. 
 

Professor Greenline from BrightChamps

What are Decimals?

Using a decimal point (.), we separate whole numbers from the fractional part of a decimal number. The numbers to the right of the decimal point are called decimal places, and the numbers to the left are whole numbers or integers. The place values of whole numbers start from ones, then move to tens, hundreds, thousands, and so on. Each place value is ten times more than the previous number. However, the place values of decimal numbers start from tenths, hundredths, and thousandths. A decimal number can be read using the term “point.” For example, 68.54 is read as sixty-eight point five four. The given table represents the place values of decimal numbers. 
 

 

Thousands

Hundreds

Tens

Ones

Decimal
Point

Tenths

Hundredths

Thousandths

Numbers

  6 7 3   7 8 9 673.89
1 0 7 8   3 5 0 1078.35
    0 5   0 8   45.08

 

Professor Greenline from BrightChamps

What are Fractions?

A portion of a whole is represented by a fraction, which is in the form a/b, where a is the numerator and b is the denominator. The numerator shows how many parts we have, while the denominator shows how many equal parts the whole is divided into. For example, 1/5, 3/8, and 7/9 are a few examples of fractions. 

 

 

Decimals and Fractions


We can represent every decimal number in the form of a fraction. To express a decimal number as a fraction, follow these steps: 


Step 1: Remove the decimal point and make the number a whole number.  

 

Step 2: Based on the decimal place value, write the number using the power of 10. 
For example, 0.46 is a decimal number, and the place value of the decimal places is in hundredths. So we can write this number as a fraction: 
0.46 = 46/100. 
If possible, we can simplify the fraction to its lowest form by finding the greatest common divisor of both numerator and denominator. Thus, 46/100 can be simplified to 23/50.
46/100 = 23/50 
We can also convert a recurring decimal to a fraction. For instance, we can write 0.444….as 4/9. 
Similarly, we can convert a fraction to a decimal by using the long division method or multiplication method. In the long division method, we divide the numerator by the denominator. However, in the multiplication method, we multiply both the numerator and denominator by a number that makes the denominator a power of 10. Then, the result will be written as a decimal.

 

For example, we can convert 3/5 into a decimal: 

 


 Step 1: To make the denominator a power of 10, multiply the numerator and denominator by 2. 
   (3 ×2 ) / (5 × 2) = 6/10 

 

 

Step 2: 6 divided by 10 gives 0.6. Hence, write the answer in the decimal form.
Thus, 3/5 = 0.6

Additionally, we can convert a fraction to a decimal by direct division. For example, convert 3/5 into a decimal:
  3 ÷ 5 = 0.6 

 

 

Decimals and Percentages 


Just like fractions, we can represent every decimal as a percentage. To compare two numbers easily, we  can convert the decimals to percentages. To convert a decimal to a percentage, follow these steps:

 

Step 1: Multiply the decimal number by 100.

 

 

Step 2: Place the % symbol on the answer. 
For instance, we can convert 0.67 to a percentage. 
      0.67 × 100 = 67%

 

We can also convert a percentage into a decimal by following these steps: 


Step 1: Divide the given percentage by 100. 

 

 

Step 2: Remove the % symbol.   
For example, we can convert 56% to a decimal. 
      56 ÷ 100 = 0.56 

Professor Greenline from BrightChamps

How to Read Decimal Fraction?

To read a decimal, start with the numbers on the left of the decimal point. If there is no number or it is zero, we read the decimal part separately. For example, we read 235.87 as two hundred thirty-five point eight seven. After the decimal point, instead of combining the values of the digits, we read each digit individually after the decimal point. Similarly, we read 0.45 as zero point four five.   

 

 

How to Represent Decimal Fraction? 


In a decimal fraction, we write the fraction without its denominator by using a decimal point. The denominator of a decimal fraction is a power of 10. We can represent a decimal fraction as a fraction and the denominator will be a power of 10, such as 10, 100, 1000, etc. For example, 


0.7 = 7/10 
Furthermore, a decimal point can be used to represent a decimal fraction. For instance, 
30/100 = 0.30.
A decimal fraction can also be expressed in words. For instance, 0.56 is read as “fifty-six hundredths” because it represents 56/100. 

 

 

What are the Operations on Decimal Fractions?


We can perform the four basic mathematical operations: addition, subtraction, multiplication, and division, on decimals. 


Addition of decimal fraction: When we add two fractions together, we must first convert them into a decimal form. 
For example, add 35/100 and 35/1000.
35/100 = 0.35 
35/1000 = 0.035
Now we can easily add the decimals. 
    0.35 + 0.035 = 0.385 

 

Subtraction of decimal fractions: If we need to subtract fractions, we must convert them into decimal forms. 
For instance, subtract 35/1000 from 35/100. 
35/1000 = 0.035
35/100 = 0.35
Now, we can easily subtract the two decimals. 
      0.35 - 0.035 = 0.315 

 

Multiplication of decimal fraction: Depending on how many zeros there are in the power of 10, move the decimal point to the right when multiplying a decimal fraction.
For example, multiply 4.4321 × 100 = 443.21
Here, the power of 10 (100) has two zeros, so we move the decimal two places to the right.

 

Division of decimal fractions: Depending on how many zeros there are in the power, move the decimal point to the left when dividing a decimal fraction by a power of 10.
For instance, 4333.4 ÷ 100 = 43.334
Here, we shift the decimal two places to the left.  

 

 


What are the Types of Decimal Fractions?


The two main types of decimals are: 
Terminating decimal 
Non-terminating decimal 


a) Repeating decimal 
b) Non-repeating decimal 


Now, let us understand each of them in detail. 


Terminating decimal: The digits after the decimal point of a terminating decimal are limited and do not continue indefinitely. For example, 1.4, 2.54, 4.984, etc. 

 

Non-terminating decimal: The non-terminating decimals have an infinite number of digits after the decimal point. It goes infinitely and may or may not repeat again and again. For instance, 1.8666…, 4.782118…etc

 

Repeating decimals: The numbers after the decimal point of a repeating decimal follow a pattern in which the digits repeat endlessly. For example, 1. 323232…, 1.151515….etc.


Non-repeating decimals: Non-repeating decimals continue endlessly but should not follow a specific pattern. For example, 1.252552555…., 1.141441444 ... .etc. 
 

Professor Greenline from BrightChamps

Real-life Applications of Decimals and Fractions

In our daily lives, we use decimals and fractions in various situations, from counting to distributing resources fairly. Here are some real-world applications of decimals and fractions: 

 

 

  • In finance and banking, decimals and fractions are used to represent money accurately, such as $45.50 cents. Additionally, bankers use fractions and decimals to calculate interest rates, loan amounts, and savings balances for account holders. For example, if a bank offers 2.5% annual interest on a savings account, it means customers can earn $2.50 for every $100 saved each year.  

 

  • When we cook, we can measure ingredients precisely using fractions and decimals. For example, baking a cake requires 1/5 cup of flour and 1.5 liters of milk, and measuring them in decimals and fractions ensures an exact measurement. 

 

  • Companies and stores calculate the price of items with discounts, offers, and taxes, such as 25% off or a $45 discount. Fractions are used to divide items fairly, such as dividing a 10-pack of items into 1/2 and 1/4 portions. 

 

  • In sports, coaches and players can track performance using decimal values that show accurate timing and scores. For example, an athlete completes a 100 m sprint in 8.39 seconds helps coaches and players to figure out areas for improvement.  
     
Max Pointing Out Common Math Mistakes

Common Mistakes and How to Avoid Them on Decimals and Fractions

Understanding the concept and properties of decimals and fractions helps make mathematical problems and calculations simpler and easier. Here are some common mistakes and helpful solutions to avoid errors: 

Mistake 1

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Forgetting to Convert Fractions Before Addition and Subtraction 
 

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Students should convert the fractions to decimal form first before performing addition and subtraction. If they forget to convert the fractions, they might get confused and end up with wrong answers. For example, 
    35/100 + 35/1000 
Students mistakenly write it as: 35 + 35 / 100 + 1000 
  = 70/1100. This is incorrect. 
The correct answer is: 
35/100 
   35 ÷ 100 = 0.35
35/1000 
    35 ÷ 1000 = 0.035
Now we can easily add the decimals. 
    0.35 + 0.035 = 0.385 
 

Mistake 2

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 Incorrectly Placing the Decimal Point 
 

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 Kids should remember to move the decimal point to the right when multiplying decimal fractions. However, move the decimal point to the left when performing the division of decimal fractions. The decimal places moved according to the number of zeros in the power of 10. 
For example, multiply 4.4321 × 100 = 443.21
Here, the power of 10, (100) has two zeros, so we move the decimal two places to the right. 
 

Mistake 3

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 Incorrect Conversion of a Decimal to a Percentage 
 

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Students should follow these steps when they convert a decimal to a percentage. 
Step 1: Multiply the decimal number by 100.
Step 2: Place the % symbol on the answer. 
For instance, if they convert 0.77 to a percentage. 
      0.77 × 100 = 77%
If kids skip any of the steps, they will get the wrong percentage. 
 

Mistake 4

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Confusion Between Terminating and Non-terminating Decimals 
 

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Remember to learn the differences and concepts between terminating and non-terminating decimals before converting them into fractions. A terminating decimal has a finite number of digits after the decimal point whereas, the digits after the decimal point of non-terminating decimals continue endlessly. For example,  
Terminating decimals: 1.4, 2.54, etc.
Non-terminating decimals: 1.8666…, 4.782118…etc.  
 

Mistake 5

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Skipping Decimal Point in the Result 
 

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 When multiplying decimal numbers, remove the decimal point and write the given numbers as whole numbers. Then perform multiplication, and after that, they should be careful to add the decimal point to the final result by counting the total decimal places in the original decimal numbers. If they forget to add the decimal point, then the answer becomes incorrect. For example, 
0.2 × 0.4 = 8. This is incorrect. 
The correct answer is: 
 

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Solved Examples of Decimals and Fractions

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Max, the Girl Character from BrightChamps

Problem 1

Mary bought 100 oranges from the store, but she later found out that 9 of them were rotten. What fraction and decimal represent the rotten oranges compared to the total oranges?

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 Fraction: 9/100
Decimal: 0.09
 

Explanation

 Total number of oranges = 100
Number of rotten oranges = 9 
To find the fraction of rotten oranges compared to the total number of oranges, we can write it as:
   Rotten oranges / Total oranges = 9/100 
The fraction 9/100 is in its simplest form because 9 and 100 have no common factors other than 1. 
Now we can convert the fraction to a decimal. So, divide 9 by 100:   
  9 ÷ 100 = 0.09 
Thus, the fraction of rotten oranges compared to the total oranges is 9/100, and in decimal form, it is 0.09. 
 

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Max, the Girl Character from BrightChamps

Problem 2

Victoria ran 4.2 km on Sunday and 6.5 km on Monday. What fraction of her total distance did she run on Sunday, and what is the decimal equivalent?

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Fraction: 42/107
Decimal form: 0.3925 (approximate value)
 

Explanation

Victoria ran 4.2 km on Sunday and 6.5 km on Monday.
So, the total distance is:
  4.2 + 6.5 = 10.7 km 
Next, we can find the fraction of the distance run on Sunday.
  Distance on Sunday / Total distance = 4.2/10.7 
4.2/10.7 is the fraction.

Now we can convert 4.2 and 10.7 into fractions: 
 4.2 = 42/10
10.7 = 107/10
We can divide the fractions. 
42/10 ÷ 107/10 
 4210   ÷ 10710  = 4210  × 10107 
Next, multiply the numerators and denominators: 
42 × 1010 × 107   = 4201070  
Now we can simplify the fraction by dividing both the numerator and denominator by its greatest common divisor (GCD) of 420 and 1070.
So, the prime factorization of 420 is:
420 = 2 × 2 × 3 × 5 × 7 
1070 = 2 × 5 × 107 
2 and 5 are the common factors, and the GCD is 10.
Next,  we can simplify the fraction: 
 4201070   ÷ 1010  = 42 107   
Now, we can convert the fraction into decimal form. So, we can divide 42 by 107:
    42 ÷ 107 ≈ 0.3925 
Thus, Victoria ran about 39.25% of the total distance on Sunday. 

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Max, the Girl Character from BrightChamps

Problem 3

A school library has 1000 books, out of which 340 are History books. What fraction of the total books are history books, and what is the decimal equivalent?

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 Fraction: 17/50 
Decimal form: 0.34
 

Explanation

Total number of books in the library = 1000
Number of History books = 340
Now we can find the fraction of books that are History books: 
Number of History books / Total number of books = 340/1000
To simplify the fraction, we must find the greatest common divisor of 340 and 1000. 
Prime factorization of 340 = 2 × 2 × 5 × 17
Prime factorization of 1000 = 2 × 2 × 2 × 5 × 5 × 5
Hence the GCD is 20.
Next, we can divide both the numerator and denominator by 20: 
   3401000  ÷ 2020  = 1750
Thus, the simplified fraction is 1750 
Next, we can convert the fraction to decimal. So, divide 17 by 50:
  17 ÷ 50 = 0.34
34% of the total books in the library are History books. 
 

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Max, the Girl Character from BrightChamps

Problem 4

Allen made 20 cakes and sold 14 of them. What fraction and decimal of the total cakes were sold?

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Fraction of cakes sold: 7/10
Decimal form: 0.7
 

Explanation

Total cakes made by Allen = 20
Cakes sold by Allen = 14
The fraction of cakes that were sold is: 
   Cakes sold / Total cakes = 14/20
To simplify the obtained fraction, we must divide both the numerator and denominator by its greatest common divisor.
Prime factorization of 14 = 2 × 7 
Prime factorization of 20 = 2 × 2 × 5
Thus, the GCD is 2. 
Next, we can divide 14 and 20 by 2:
   1420  ÷ 22 = 710 
The simplified fraction of 14/20 is 7/10.
Now we can convert a fraction to a decimal form.
Divide 7 by 10: 
   7 ÷ 10 = 0.7
Therefore, Allen sold 70% of the total cakes.
 

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Max, the Girl Character from BrightChamps

Problem 5

Philip bought 30 chocolate bars and gave 15 to his friends. What fraction of the chocolates did he give away, and what is the decimal equivalent?

Ray, the Boy Character from BrightChamps Saying "Let’s Begin"

 Fraction: 1/2 
Decimal form: 0.5
 

Explanation

Total chocolate bars Philp bought = 30 
Chocolate bars given to his friends = 15 
Now we can find the fraction of chocolates given to his friends is: 
   Chocolate given away / Total chocolates = 15/30
Next, simplify the obtained fraction by finding its greatest common divisor (GCD) of 15 and 30. 
The factors of 15 are 1, 3, 5, and 15
The factors of 30 are 1, 2, 3, 5, 6, 10, 15, and  30 
Hence the GCD is 15.
Here, we can divide the numerator and denominator by 15.
  1530  ÷ 1515   = 12
So, the fraction of chocolates given away is, 12 
Next, we can convert the fraction into a decimal form.  
Divide 1 by 2: 
   1 ÷ 2 = 0.5 
Hence, Philip gave away 50% of the chocolates to his friends.  
 

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FAQs on Decimals and Fractions

1.What do you mean by decimals and fractions?

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2.How to read 234.76 and 1786.656 in decimal form?

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3.How to convert fractions into decimals?

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4.How may decimals be converted to percentages?

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5.Differentiate repeating and non-repeating decimals.

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6.How can children in United Arab Emirates use numbers in everyday life to understand Decimals and Fractions?

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7.What are some fun ways kids in United Arab Emirates can practice Decimals and Fractions with numbers?

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8.What role do numbers and Decimals and Fractions play in helping children in United Arab Emirates develop problem-solving skills?

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9.How can families in United Arab Emirates create number-rich environments to improve Decimals and Fractions skills?

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Hiralee Lalitkumar Makwana

About the Author

Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.

Max, the Girl Character from BrightChamps

Fun Fact

: She loves to read number jokes and games.

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