Difference between Terminating and Recurring Decimals
July 18, 2023 | by Bloom Code Studio
| Terminating Decimals | Repeating Decimals |
| If the decimal expression of a/b terminates. i.e. comes to an end, then the decimal so obtained is called Terminating decimals. | A decimal in which a digit or a set of digits repeats repeatedly periodically is called a repeating decimal. |
| Example: ¼ =0.25 | Example: ⅔ = 0.666… |
Some Special Characteristics of Rational Numbers
- Every Rational number is expressible either as a terminating decimal or as a repeating decimal.
- Every terminating decimal is a rational number.
- Every repeating decimal is a rational number.
Irrational Numbers
- The non-terminating, non-repeating decimals are irrational numbers.
Example: 0.0100100001001…
- Similarly, if m is a positive number which is not a perfect square, then √m is irrational.
Example: √3
- If m is a positive integer which is not a perfect cube, then 3√m is irrational.
Example: 3√2
Properties of Irrational Numbers
- These satisfy the commutative, associative and distributive laws for addition and multiplication.
- Sum of two irrationals need not be irrational.
Example: (2 + √3) + (4 – √3) = 6
- Difference of two irrationals need not be irrational.
Example: (5 + √2) – (3 + √2) = 2
- Product of two irrationals need not be irrational.
Example: √3 x √3 = 3
- The quotient of two irrationals need not be irrational.
2√3/√3 = 2
- Sum of rational and irrational is irrational.
- The difference of rational and irrational number is irrational.
- Product of rational and irrational is irrational.
- Quotient of rational and irrational is irrational.
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