Decimals and Fractions
2026-02-21 20:40 Diff
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Last updated on December 10, 2025

Both whole numbers and fractions 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. In this article, we will learn about the concepts and properties of decimals and fractions in detail.

What is a Decimal Fraction?

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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.

Example:

  • 0.7 (\(\frac{7}{10}\))

  • 0.23 (\(\frac{23}{100}\))

  • 0.009 (\(\frac{9}{1000}\))

  • 5.4 (\(\frac{54}{10}\))

What are Decimals?

A decimal point (.) separates whole numbers from the fractional part of a 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. 

What are Fractions?

A fraction is a mathematical way to represent equal parts of a whole or a collection. It consists of two distinct numbers separated by a line (called a vinculum):

  • The Numerator (Top Number): This number shows how many parts you are counting or have selected.
  • The Denominator (Bottom Number): This number shows the total number of equal parts the whole is divided into.


Examples:

  • 1/5 (One part out of five)
  • 3/8 (Three parts out of eight)
  • 7/9 (Seven parts out of nine)

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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: 

\(0.46 = \frac{46}{100} \)

If possible, we can simplify the fraction to its lowest form by finding the greatest common divisor of both numerator and denominator. Thus, \(\frac{46}{100} \) can be simplified to \(\frac{23}{50} \).

\(\frac{46}{100} = \frac{23}{50} \)

We can also convert a recurring decimal to a fraction. For instance, \(0.444\ldots = \frac{4}{9} \).

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.

Example

We can convert \(\frac{3}{5} \) into a decimal: 

Step 1: To make the denominator a power of 10, multiply the numerator and denominator by 2. 

\(\frac{3 \times 2}{5 \times 2} = \frac{6}{10} \)

Step 2: 6 divided by 10 gives 0.6. Hence, write the answer in the decimal form.

Thus, \(\frac{3}{5} = 0.6 \)

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. 

Example:

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.

Example:

We can convert 56% to a decimal.

56 ÷ 100 = 0.56 

How to Read Decimal Fraction?

To read a decimal number, start by reading the whole number to the left of the decimal point, normally. If the whole number is zero, you can simply say 'zero.' Next, read the decimal point as the word 'point.' Finally, read the digits to the right of the decimal point individually, one by one. For instance, 235.87 is read as 'two hundred thirty-five point eight seven'—never as 'eighty-seven.' Similarly, 0.45 is read as 'zero point four, five'.

Examples:
Here are a few more examples showing how this rule applies to different types of decimals:
 

  • Whole number with a decimal:
    • 15.2 \(\rightarrow\) Fifteen point two
    • 7.14 \(\rightarrow\) Seven point one four
       
  • Decimals starting with zero:
    • 0.3 \(\rightarrow\) Zero point three
    • 0.99 \(\rightarrow\) Zero point nine nine
       
  • Decimals with placeholders (zeros in the middle):
    • 6.05 \(\rightarrow\) Six point zero five
    • 12.001 \(\rightarrow\) Twelve point zero zero one

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.

Example:

\(0.7 = \frac{7}{10} \)

Furthermore, a decimal point can be used to represent a decimal fraction. For instance, 

\(\frac{30}{100} = 0.30 \).

A decimal fraction can also be expressed in words. For instance, 0.56 is read as “fifty-six hundredths” because it represents \(\frac{56}{100} \).

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 \(\frac{35}{100} \) and \(\frac{35}{1000} \).

 
\(\frac{35}{100} = 0.35 \)

\(\frac{35}{1000} = 0.035 \)

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 \(\frac{35}{1000} \) from \(\frac{35}{100} \).

\(\frac{35}{1000} = 0.035 \)

\(\frac{35}{100} = 0.35 \)

Now, we can easily subtract the two decimals. 

0.35 - 0.035 = 0.315 

Multiplication of decimal fraction: When multiplying a decimal by a power of 10, move the decimal point to the right by as many places as there are zeros. 

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: When dividing a decimal by a power of 10, move the decimal point to the left by as many places as there are zeros.

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 types of decimals are: 

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.

Tips and Tricks to Master Decimals and Fractions

Fractions and decimals are essentially two different languages used to describe the exact same thing: parts of a whole. Helping students realize that these are connected concepts rather than isolated topics is the key to building mathematical fluency. Instead of memorizing rules blindly, building a strong conceptual foundation allows learners to switch between the two forms effortlessly. Here are a few tips and tricks to help navigate these concepts.

  • Use Money as a Concrete Model: Money is the most intuitive real-world application where decimal and fractions coexist naturally. Explain that a quarter is named "quarter" because it is literally 1/4 of a dollar, which is written as 0.25. Using physical coins to build a dollar helps learners visualize that decimals represent specific fractional parts of a whole unit.
     
  • Read Decimals by Place Value: Discourage reading 0.5 as "zero point five" and instead encourage reading it as "five-tenths." When the number is spoken using its proper place value name, the conversion from decimal to fractions becomes auditory and automatic. If a student hears "five-tenths," they can easily write down 5/10 without needing a conversion formula.
     
  • The Division Bar Visualization: To simplify the process of changing fractions to decimal, remind students that the line separating the numerator and denominator is actually a division symbol. A helpful visual trick is to imagine the top number (numerator) "falling" into the division box (inside the house), while the bottom number (denominator) stays outside. This reinforces that 3/4 is simply the calculation \(3 \div 4\).
     
  • Focus on Base-10 Denominators: Before tackling complex numbers, ensure there is a mastery of decimal fractions—fractions specifically with denominators of 10, 100, or 1000. Using a 10 \times 10 grid helps visualize that coloring 7 columns is 70/100, which is 0.70. Mastering these "friendly" fractions bridges the gap between the two concepts.
     
  • The Double Number Line: Draw two parallel number lines, marking one with fractions (0, 1/4, 1/2, 3/4, 1) and the other directly beneath it with decimals (0, 0.25, 0.5, 0.75, 1.0). Seeing that these numbers occupy the exact same physical space on the line reinforces that decimal and fractions are equal values, just written differently.
     
  • Memorize the "Famous Families": Just like multiplication tables, certain conversions should be memorized for speed. Create "families" of benchmarks to memorize: the "Halves" (0.5 = 1/2), the "Quarters" (0.25 = 1/4), and the "Fifths" (0.2 = 1/5). Knowing these anchors makes estimating complex fractions to decimal conversions much less intimidating.
     
  • The "Zeros" Trick for Expansion: When converting decimal to fractions, the number of digits behind the decimal point tells you how many zeros belong in the denominator. For example, in 0.45, there are two digits after the point, so the fraction is over 100 (45/100). In 0.125, there are three digits, so it is over 1000 (125/1000). This eliminates the guesswork of whether to use 10, 100, or 1000.

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: 

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: 
 

  • Finance and banking: Decimals and fractions are used to represent money accurately, such as $45.50. 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.  
     
  • Cooking: 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. 
     
  • 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.
     
  • Engineering and construction: Decimal fractions are used in construction for precise cut of materials. For example, 2.75 mm rod, 2.5m beam, etc.

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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?

Okay, lets begin

Fraction: \(\frac{9}{100} \)

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:

\(\frac{\text{Rotten oranges}}{\text{Total oranges}} = \frac{9}{100} \)

The fraction \(\frac{9}{100} \) 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 \(\frac{9}{100} \), and in decimal form, it is 0.09. 

Well explained 👍

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?

Okay, lets begin

Fraction: \(\frac{42}{107} \)

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. 

4.2/10.7 = (42/10) ÷ (107/10) = 42/107

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 (rounded to 4 decimal places)

Thus, Victoria ran about 39.25% of the total distance on Sunday.

Well explained 👍

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?

Okay, lets begin

Fraction: \(\frac{17}{50} \)

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: 

\(\frac{\text{Number of History books}}{\text{Total number of books}} = \frac{340}{1000} \)

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. 

Well explained 👍

Problem 4

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

Okay, lets begin

Fraction of cakes sold: \(\frac{7}{10} \)

Decimal form: 0.7

Explanation

Total cakes made by Allen = 20

Cakes sold by Allen = 14

The fraction of cakes that were sold is: 

\(\frac{\text{Cakes sold}}{\text{Total cakes}} = \frac{14}{20} \)

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 \(\frac{14}{20} \) is \(\frac{7}{10} \).

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.

Well explained 👍

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?

Okay, lets begin

Fraction: \(\frac{1}{2} \)
Decimal form: 0.5
 

Explanation

Total chocolate bars Philip bought = 30 

Chocolate bars given to his friends = 15 

Now we can find the fraction of chocolates given to his friends is: 

\(\frac{\text{Chocolate given away}}{\text{Total chocolates}} = \frac{15}{30} \)

Next, simplify the fraction by finding the 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.

15 ÷ 15 = 1, 30 ÷ 15 = 2. So, fraction = \(\frac{1}{2} \).

So, the fraction of chocolates given away is,  \(\frac{1}{2} \)

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.

Well explained 👍

FAQs on Decimals and Fractions

1.What do you mean by decimals and fractions?

A decimal number separates a whole number from a fractional part using a decimal point. A fraction represents a portion of a whole and is written as a/b. A fraction contains a numerator (top number) and a denominator (bottom number). For example,
Decimals:  2.67, 1.76, and 4.987…etc.
Fraction: \(\frac{3}{9}, \frac{1}{4}, \frac{10}{12} \)…etc.

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

We can read a decimal number using the term “point” for the decimal point. Hence, 234.76 is read as two hundred thirty-four point seven six. Also, 1786.656 is read as one thousand seven hundred eighty-six point six five six. 

3.How to convert fractions into decimals?

To convert a fraction to a decimal, we must divide the numerator by the denominator. We can easily convert a fraction into a decimal by the direct division method. For example, to convert \(\frac{2}{5} \) into a fraction: 
2 ÷ 5 = 0.4 

4.How may decimals be converted to percentages?

We can convert a decimal to a percentage, by following these steps: 
Step 1: Multiply the decimal number by 100.
Step 2: Place the % symbol to the answer. 
For example, convert 0.57 to a percentage. 
0.57 × 100 = 57%

5.Differentiate repeating and non-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 continue endlessly but should not follow a specific pattern. For example, 1.252552555…., 1.141441444 ... .etc. 

6.At what age should my child learn decimal fraction?

Typically, decimal and fractions are introduced in grades 4 to 6. Children should first become comfortable with fractions and basic division.

7.How can I explain decimals and fractions easily?

Try to relate them to money, measurements, or quantities. Show to them that tenths, hundredths, thousandths are a part of a whole.

8.How can I make learning decimals and fractions fun?

Use some of the real-life situations to teach them. That will help them access more knowledge. For example, use problems related to money, measurements, recipes, etc.

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.

Fun Fact

: She loves to read number jokes and games.