Non Terminating Decimals

In this page we are going to discuss about Non terminating decimals.Below we will get introduction to Non terminating decimals. A non terminating decimal is one of the type of decimals which are divided into two types. They are,

Terminating Decimals
Non terminating Decimals

Non terminating Decimals is the continuous decimal number. It has been going on till the value infinitive. It is the very big value sometimes these non terminating decimals are rounded to its nearest values. But the Terminating decimal number is the fixed value of the decimal value.

Calculating Non Terminating Decimals

Below you can see the steps of calculating non terminating decimals:

Divide 5/3

Step 1: This is the type of an improper fraction. because here numerator takes the large value than the denominator.

Step 2: One time 3 is 3. So the remainder is 2 and the quotient value is 1

Step 3: Now 2 is not divided by 3

Step 4: So we can add zero to the remainder 2 and put a point the quotient value 1

Step 5: Now the value is 20. Again we can do the same procedure

Step 6: Now 6 times 3 is 18 again the remainder is 2 and the quotient value is 6

Step 7: Again we can add zero to 2 then the value is 20

Step 8: Again 6 times 3 is 18. Again the remainder is 2 and the quotient value is 6

Step 9: Now the decimal value is 1.66 …….its going on

Step 10: This decimal part 1.66……is known as the non terminating decimal.

Step 11: It can be rounded as 1.67

Step 12: Because it’s decimal part value is greater than or equal to 5. So the value of the last decimal value is consider as one and that value is added to the previous decimal value.

Step 13: Otherwise the last decimal part value is less than five. So the value of the last decimal value is simply leave. And the previous decimal value is considered as the last decimal digit value.

Pictorial Representation of this problem is shown below:

Non- terminating decimals

Practice problems

Here are some practice problems on non terminating Decimals:

Identify which of the fractions gives the non terminating decimals:

(4)/(2)
(2)/(3)
(6)/(3)

Answer:

Terminating decimals (4)/(2) =2 and (6)/(3) =2

Non terminating decimal (2)/(3) = 0.6666.....