103 LearnersLast updated on July 5th, 2025
Terminating Decimal
The word “terminate” comes from Latin and means to bring to an end or cease. Terminating decimals are decimal numbers that end after a certain number of digits. In short, the numbers after the decimal point will be finite or terminating.
What is a Terminating Decimal?
Decimals represent the partial amount of a whole number. These decimals are of two types, terminating decimals and non-terminating decimals. Terminating decimals are those decimal numbers where the values after the decimal point come to an end. For example, if we divide 1/4 we get 0.25, which is a terminating decimal because it ends after two decimal places.
What is a Non-Terminating Decimal?
Non-terminating decimals are those decimal numbers that do not end after some decimal value. These are then again divided into two categories: non-terminating recurring decimal expansion and non-terminating non-recurring decimal expansion. Let’s say for 1/3 and 3.
How to Identify a Terminating Decimal?
You can determine whether a decimal number is terminating by checking the following conditions:
- The terminating decimal will always have finite numbers after the decimal point. That means the number will stop after some digits.
- All terminating decimals are rational numbers.
- Fractions that have denominators in the form 2m × 5n, where m and n are non-negative integers, will have terminating decimal expansions.
- If the denominator of a fraction is in the form of 2m 5n, where m and n are positive integers, then it has a terminating decimal expansion.
Tips and Tricks for Terminating Decimals
Identifying terminating decimals can be easy if you know the right tricks. Here are some simple tips to help you quickly recognize and remember them.
- Check the denominator: A fraction p/q has a terminating decimal only if the denominator contains only the prime factors 2 and/or 5 (e.g., 1/8 = 0.125, 1/25 = 0.04).
- Divide and observe: If a fraction converts into a decimal that stops after a few digits, it is terminating. If it keeps going with a pattern, it is a non-terminating recurring decimal.
- Use prime factorization: Factorize each denominator and check whether it contains 2 and/or 5 as its factors. If yes, then it is terminating, otherwise it is non-terminating.
- Memorize Common Examples: Knowing simple terminating decimals can help you recognize patterns. For example, 1/2, 3/8, 1/4, etc.
- Practice with Division: Convert fractions to decimals using long division. The long division reveals whether the decimal terminates or repeats to find whether the decimal number is terminating or non-terminating.
Real-Life Applications of Terminating Decimals
Terminating decimals are not just used in math class, they play an important role in everyday life. From money and measurements to science and sports, these decimals help us make accurate calculations in various real-world situations.
- Money and Currency: Prices, payments, and financial transactions frequently involve terminating decimals, such as $4.75 or $99.50, since currency values are typically limited to two decimal places in most countries.
- Measurements: Length, weight, and volume are often expressed as terminating decimals in practical applications, such as 2.5 meters, 1.75 liters, and 3.2 kilograms
- Time Calculation: Time is sometimes represented in decimal forms, such as 1.5 hours (1 hour 30 minutes) or 2.75 hours (2 hours 45 minutes), to schedule, work hours, or travel durations.
Common Mistakes of Terminating Decimals and How to Avoid Them
Understanding decimals that terminate is important for students while learning. This is because it makes their calculations easier. However, students often make mistakes in identifying them. Here are five common mistakes that students might make and how to avoid them.
Mistake 1
Expecting that all fractions will terminate while doing the calculation
Some students, while converting fractions to decimals, expect that the decimals will always terminate. Remember that only fractions with denominators having 2 and/or 5 as prime factors will terminate.
Mistake 2
Thinking that long decimal numbers are always non-terminating.
Some students by looking at the decimal length conclude answers whether it is non-terminating. You should understand that some decimals look long, but eventually stop. Always make sure you check if the decimal ends or repeats before assuming it is non-terminating.
Mistake 3
Ignoring that all terminating decimals are rational numbers.
Mistaking that all decimals are irrational numbers is quite common in students. Always remember that terminating decimals are always rational because they can be written as fractions (p/q). Only non-terminating, non-repeating decimals are irrational.
Mistake 4
Ignoring or forgetting to simplify fractions before checking for termination.
Always remember to simplify the fractions first and then go for the division. A fraction like 6/24 looks like it has a denominator of 24 (not just 2s and 5s), but when simplified to 1/4, it is terminating.
Mistake 5
Not able to confirm if a decimal number is terminating or non-terminating.
A terminating decimal stops completely, while a recurring decimal (like 0.333…) repeats forever. Always look for a clear stopping point to identify terminating decimals correctly.
Solved Examples for Terminating Decimals
Problem 1
Is 7/20 a terminating decimal?
Yes, 7/20 = 0.35 is a terminating decimal.
Explanation
The denominator 20 has prime factors 2 × 2 × 5, which are only 2s and 5s, so the decimal terminates.
Problem 2
Convert 5.6 into a fraction and check if it is a terminating decimal.
5.6 = 5610 = 285, which is a terminating decimal.
Explanation
When we divide 28 by 5, we get 5.6, which ends after one decimal place, so it is a terminating decimal.
Problem 3
Jake has 8 chocolates, and he shares them equally among 5 friends. How many chocolates does each friend get?
Each friend gets 1.6 chocolates.
Explanation
Dividing 8 by 5 gives 1.6, which stops after one decimal place, so it is a terminating decimal.
Problem 4
Express 78 as a decimal.
78 = 0.875
Explanation
Dividing 7 by 8 results in 0.875, which ends after three decimal places, making it a terminating decimal.
Problem 5
Is 0.48 a terminating decimal?
Yes, 0.48 is a terminating decimal.
Explanation
The decimal 0.48 has only two decimal places and does not go on forever, so it is a terminating decimal.
FAQs Related to Terminating Decimals
1.How can I identify if a fraction has a terminating decimal?
2.Is every rational number a terminating decimal?
3.Can a whole number be a terminating decimal?
4.What is the difference between a terminating and a repeating decimal?
5.Can an irrational number be a terminating decimal?
6.How can children in United States use numbers in everyday life to understand Terminating Decimal?
7.What are some fun ways kids in United States can practice Terminating Decimal with numbers?
8.What role do numbers and Terminating Decimal play in helping children in United States develop problem-solving skills?
9.How can families in United States create number-rich environments to improve Terminating Decimal skills?
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.
