write 10 examples each of terminating and non terminating and decimals which neither treminates nor recurring
Answers
Step-by-step explanation:
Rational numbers can be expressed in the form of decimal fractions. These rational numbers when converted into decimal fractions can be both terminating and non-terminating decimals.
Terminating decimals: Terminating decimals are those numbers which come to an end after few repetitions after decimal point.
Example: 0.5, 2.456, 123.456, etc. are all examples of terminating decimals.
Non terminating decimals: Non terminating decimals are those which keep on continuing after decimal point (i.e. they go on forever). They don’t come to end or if they do it is after a long interval.
For example:
π = (3.141592653589793238462643383279502884197169399375105820974.....) is an example of non terminating decimal as it keeps on continuing after decimal point.
If a rational number (≠ integer) can be expressed in the form p2n×5m, where p ∈ Z, n ∈ W and m ∈ W, the rational number will be a terminating decimal. Otherwise, the rational number will be a nonterminating, recurring decimal.
For example:
(i) 58 = 523×50. So, 58 is a terminating decimal.
(ii) 91280 = 928×51. So, 91280 is a terminating decimal.
(iii) 445 = 432×51. Since it is not in the form \(\frac{p}{2^{n} × 5^{m}}\), So, 445 is a non-terminating, recurring decimal.
For example let us take the cases of conversion of rational numbers to terminating decimal fractions:
(i) 12 is a rational fraction of form pq. When this rational fraction is converted to decimal it becomes 0.5, which is a terminating decimal fraction.
(ii) 125 is a rational fraction of form pq. When this rational fraction is converted to decimal fraction it becomes 0.04, which is also an example of terminating decimal fraction.
(iii) 2125 is a rational fraction form pq. When this rational fraction is converted to decimal fraction it becomes 0.016, which is an example of terminating decimal fraction.
Now let us have a look at conversion of rational numbers to non terminating decimals:
(i) 13 is a rational fraction of form pq. When we convert this rational fraction into decimal, it becomes 0.333333… which is a non terminating decimal.
(ii) 17 is a rational fraction of form pq. When we convert this rational fraction into decimal, it becomes 0.1428571428571… which is a non terminating decimal.
(iii) 56 is a rational fraction of form pq. When this is converted to decimal number it becomes 0.8333333… which is a non terminating decimal fraction.
Hope it helps
Answer
Terminating decimals are 0.5, 0.125, 0.4, 0.9 etc. Non terminating decimals are 0.3141592……, 0.3333….. and 0.666…..etc.
Explanation
- There are different categories of numbers such as integers, real numbers, natural numbers, rational and irrational numbers.
- Rational numbers are defined as the set of those real numbers which can be written as in p/q form, where q is not equal to zero.
- The rational numbers which can be further written as in the decimal form also are divided into two parts, the one is terminating and the other is non-terminating decimal numbers.
- Non-terminating numbers are further divided into the two types i.e. recurring decimal and the second one non-recurring decimal numbers.
- Terminating decimal numbers are those decimals which are terminated after some digits such as 0.5 and 0.125 etc.
- Similarly the non-terminating are those numbers which never stop after the decimals such as, 0.31415……. They go on forever.
- The recurring numbers are those numbers which have some pattern or the digits are repeated after the decimal, for example, 0.666….. and 0.47878787…..etc.
- Therefore by taking the notes of each type you can write many numbers of different types.
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