Last updated on July 25th, 2025
The exactness of decimal representation refers to whether a number has a finite decimal (ending after a few digits) or an infinite decimal (repeating or non-repeating). This concept is important in mathematics, especially in rational numbers, real numbers, and fractions.
Decimal numbers can be classified based on whether they come to an end or continue infinitely. That is, whether decimals stop after a certain number of digits, while others continue infinitely. The exactness of the decimal indicates the type of decimal number we are working with. There are two types of decimal numbers: terminating and non-terminating. Let’s understand the difference.
The decimal numbers can be categorized into two types: terminating and non-terminating. These non-terminating decimal numbers are divided into two: repeating non-terminating decimals and non-repeating non-terminating decimals.
Terminating decimals: Decimal numbers in which the digits after the decimal point come to an end after a certain number of places. For example, 15 ÷ 2 = 7.5
Non-terminating decimals: Those decimal numbers that continue infinitely without ending. Non-terminating decimals are, then again, divided into two types: repeating and non-repeating.
Repeating Non-terminating Decimals: These decimal numbers repeat a sequence of digits forever. It keeps repeating the same number or the same pattern. For example, 1 ÷ 3 = 0.33333333…, 2 ÷ 7 = 0.285714285714…
Non-repeating Non-terminating Decimals: These decimal numbers go on infinitely without ever forming a repeating pattern. For example, the mathematical constant Pi is 3.1415926535…
Irrational numbers cannot be written as fractions of two integers (ab) and have decimals that never end or repeat. Their decimal expansion continues infinitely without any repeating pattern. These are the following characteristics of irrational decimal numbers.
Here are some examples of irrational numbers and their decimal representation:
The exactness of decimal representations is important in many real-life applications where precision matters. Here are some examples showing why the exactness of decimal representation is important.
When working with decimals, students often make mistakes that might confuse terminating, repeating, and non-repeating decimals. Understanding these errors and how to avoid them helps improve accuracy in identifying different types of decimals.
Lily has $5.75, and she buys a toy for $2.50. How much money does she have left?
3.25
Subtract dollars and cents carefully.
5 dollars minus 2 dollars = 3 dollars
75 cents minus 50 cents = 25 cents
Thus, Lily has $3.25 left.
A recipe needs 2.5 cups of flour, but Alex accidentally adds only 2.25 cups. How much more flour does he need to add?
0.25 cups
To find the missing amount, we must subtract 2.25 from 2.5.
Then converting to fractions:
2.5 = 212 = 2.50
2.25 stays the same
2.50 – 2.25 = 0.25 (¼ cup)
Thus, Alex needs to add ¼ cup more.
In the morning, the temperature was 18.6° C, and in the afternoon, it rose to 22.3° C. How much did the temperature increase?
22.3 – 18.6 = 3.7° C
Subtract the morning temperature from the afternoon temperature.
22.3 – 18.6 = 3.7° C
So, the temperature rose by 3.7 °C.
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.
: She loves to read number jokes and games.