Decimal Expansions Of Rational Numbers In Terms Of Terminating Non Note: if a rational number (≠ integer) can be expressed in the form p (2^n × 5^m) where p ∈ z, n ∈ w, and m ∈ w then the rational number will become a terminating decimal. if not, the rational number becomes the non – terminating numbers. examples of repeating and non repeating decimals. 1. If a rational number (≠ integer) can be expressed in the form p 2n×5m p 2 n × 5 m, 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 5 8 = 5 23×50 5 2 3 × 5 0. so, 58 5 8 is a terminating decimal.
Decimal Expansions Of Rational Numbers In Terms Of Terminating Non When expressing a rational number in the decimal form, it can be terminating or non terminating but repeating and the digits can recur in a pattern. example: 1 2= 0.5 is a terminating decimal number. 1 3 = 0.33333 is a non terminating decimal number with the digit 3, repeating. If the decimal expansion of a number is terminating or non terminating and recurring (repeating), then the number is a rational number. the decimal expansion of an irrational number is non terminating and non repeating. conclusion. in this article, we learned about the two types of decimal expansions of rational numbers. Example: find the decimal expansion of 3 6. here, the quotient is 0.5 and the remainder is 0. rational number 3 6 results in a terminating decimal. case 2: remainder not equal to zero. example: express 5 13 in decimal form. here, the quotient is 0.384615384 and the remainder is not zero. notice that the number…384 after the decimal is. Non terminating non recurring decimal expansion; a number has a terminating decimal expansion if the digits after the decimal point terminate or are finite. the fraction 5 10 has the decimal expansion of 0.5, which is a terminating decimal expansion because digits after the decimal point end after one digit. a rational number has either a.
Decimal Expansions Of Rational Numbers In Terms Of Terminating Non Example: find the decimal expansion of 3 6. here, the quotient is 0.5 and the remainder is 0. rational number 3 6 results in a terminating decimal. case 2: remainder not equal to zero. example: express 5 13 in decimal form. here, the quotient is 0.384615384 and the remainder is not zero. notice that the number…384 after the decimal is. Non terminating non recurring decimal expansion; a number has a terminating decimal expansion if the digits after the decimal point terminate or are finite. the fraction 5 10 has the decimal expansion of 0.5, which is a terminating decimal expansion because digits after the decimal point end after one digit. a rational number has either a. Non repeating non terminating decimal. the decimal numbers that continue forever with no digit (or group of digits) repeating. such decimals are also called non recurring or non repeating decimals. these are always irrational numbers. e.g., π = 3.141592653…, √2 = 1.4142135623…, 737.537269541…, or 1.41421356237309504…. Any rational number can either be expressed as a. terminating decimal (i.e., a decimal with a finite number of nonzero digits such as 0.4) or a repeating decimal (i.e., a decimal with a single digit or a fixed string of digits that repeats forever such as 0.333333…) expressing a fraction as a decimal (either terminating or repeating) simply.
Decimal Expansions Of Rational Numbers In Terms Of Terminating Non Non repeating non terminating decimal. the decimal numbers that continue forever with no digit (or group of digits) repeating. such decimals are also called non recurring or non repeating decimals. these are always irrational numbers. e.g., π = 3.141592653…, √2 = 1.4142135623…, 737.537269541…, or 1.41421356237309504…. Any rational number can either be expressed as a. terminating decimal (i.e., a decimal with a finite number of nonzero digits such as 0.4) or a repeating decimal (i.e., a decimal with a single digit or a fixed string of digits that repeats forever such as 0.333333…) expressing a fraction as a decimal (either terminating or repeating) simply.
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