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RATIONAL NUMBER IN DECIMAL REPRESENTATION
Every rational number can be expressed as terminating decimal or non-terminating decimal.
1. Terminating Decimal: The word "terminate" means "end". A decimal that ends is a terminating decimal.
O R
A terminating decimal doesn't keep going. A terminating decimal will have a finite number of digits after the decimal point.
Ex. Express (7 over 8) in the decimal form by long division method.
Sol.We have,
2. Non terminating & Repeating (Recurring decimal):– A decimal in which a digit or a set of a finite number of digits repeats periodically is called Non-terminating repeating (recurring) decimals.
Ex. Find the decimal representation of (8over 3)
Sol. By long division, we have
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COMPETITION WINDOW
1.
we observe that the prime factorisation of the denominators of these rational numbers is of the form 2m × 5n, where m,n are non-negative integers. Hence, (189over 125)has terminating decimal expansion. 2.
we observe that the prime factorisation of the denominator of these rational numbers is not of the form 2m × 5n, where m,n are non-negative integers. Hence (17 over 6) has non-terminating and repeating decimal expansion. |
FAQs on Decimal Expansion of Real Numbers - Terminating and Non -Terminating - Number Systems, Class 9, Math
| 1. What are terminating decimals? |  |
| 2. What are non-terminating decimals? | |
Ans. Non-terminating decimals are the decimals that do not end after a finite number of digits. These decimals either repeat the same sequence of digits or have an infinite number of digits after the decimal point. For example, 0.333..., 0.585858..., and pi (π) are non-terminating decimals.
| 3. Can a rational number have a non-terminating decimal expansion? | |
Ans. Yes, a rational number can have a non-terminating decimal expansion. For example, the fraction 1/3 can be represented as a non-terminating decimal 0.333... Similarly, the fraction 2/7 can be represented as a non-terminating decimal 0.2857142857...
| 4. Are all irrational numbers non-terminating decimals? | |
Ans. Yes, all irrational numbers have non-terminating decimal expansions. This is because irrational numbers cannot be expressed as fractions, and their decimal expansions go on infinitely without repeating. For example, the square root of 2 (√2) is an irrational number with a non-terminating decimal expansion of 1.41421356....
| 5. How can we determine if a decimal expansion is terminating or non-terminating? | |
Ans. To determine if a decimal expansion is terminating or non-terminating, we need to see if the decimal ends after a finite number of digits or not. If the decimal expansion ends after a finite number of digits, then it is a terminating decimal. If the decimal expansion goes on infinitely, then it is a non-terminating decimal. We can also look for patterns in the decimal expansion to see if it repeats the same sequence of digits or not.
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