What Is A Terminating Decimal:
1. When a decimal number ends with zero or more zero’s after the decimal point, it is called terminating Decimal. For example, 0.5, 2.7, and 7.004 are terminating decimals.
2. A number is not a terminating decimal if it does not end with zero or more zero’s after the decimal point. For example, 1.6 and 3.14159 are not terminating decimals because they do not have a final zero after the decimal point.
3. In contrast, non-terminating decimals have a final zero after the decimal point, but they go on forever without repeating themselves (or ending). For example, pi (3.14159…) is a famous non-terminating decimal that never ends!
4. Terminating decimals are easier to work with than non-terminating decimals because they only go on for a finite amount of time. For example, 0.5 and 2.7 can be expressed as fractions (1/2 and 7/10, respectively). However, we cannot express pi (3.14159…) as a fraction because it goes on forever without repeating itself!
5. Notice that the decimal point in both terminating and non-terminating decimals can be moved to different places to create new numbers. For example, 7004.(1) = 704., while 7004.(2) = 7040.. Hundreds are often dropped when placing this type of Decimal in scientific notation: 6300000m73.(6) = 630000073 m.
6. Terminating decimals are also called finite because they have a definite length that can be counted (just like integers). For example, there is no way to express the number of meters equal to 6300000m73. (6) without using an infinite amount of digits!
7. Finally, notice that non-terminating decimals are irrational numbers. This means they cannot be expressed as fractions or ratios of integers! However, like terminating decimals, their value does not change when the decimal point is moved left or right. So for instance, pi (3.14159…) = 3.14159…(2) = 3.141592…(3), and so on.
So there you have it! Terminating decimal numbers are those that end with zero or more zero’s after the decimal point, while non-terminating decimal numbers go on forever without repeating themselves.
Both decimals can be expressed in scientific notation, but terminating decimals are easier to work with because they have a finite length. Finally, irrational numbers like pi (3.14159…) are non-terminating decimals that cannot be expressed as fractions or ratios of integers. Whew! That was a lot of information! But now you know everything you need to know about terminating and non-terminating decimals.
What is non terminating decimal expansion:
In mathematics, a non-terminating decimal is an actual number expressed by an infinite sequence of digits after the decimal point without the line eventually recurring to zero.
For example, 4.56789101112131415…is a non-terminating decimal but 4.567891011…. is not as it repeats itself “4.” There are many non-terminating decimals, but only some repeating decimals are also non-repeating decimals.
Terminating Decimal:- A terminating decimal has a finite number of digits, so there is some value after which all additional digits are 0 or have been seen before in the given number representation.
For example:
3.717647058823529 is a terminating decimal because all of the additional digits are 0.
It’s easy for humans to recognize that a string is non-terminating, but it can be difficult for computers, so some algorithms have been developed to check if a number is terminating or not.
Terminating Decimal and repeating Decimal:
A terminating decimal is an actual number that a finite sequence of digits can express. There is some value after which all additional digits are 0 or seen before in the given number representation.
For example:
3.717647058823529 is a terminating decimal because all of the additional digits are 0.
It’s easy for humans to recognize that a string is non-terminating. Still, it can be difficult for computers, so some algorithms have been developed to check if a number is terminating or not.
A repeating decimal is an actual number that can be expressed as an infinite sequence of digits where the same digit appears more than once in a row. Example: 5/9=0.5555… is a repeating decimal because the five appear more than once in a row.