Is 3\/10 a non terminating and repeating?<\/p>\n\n\n\n
The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n To determine whether the fraction ( \\frac{3}{10} ) is non-terminating and repeating, we first need to understand the definitions of terminating and non-terminating decimal representations.<\/p>\n\n\n\n Terminating Decimal<\/strong>: A decimal is considered terminating if it has a finite number of digits after the decimal point. For example, ( 0.25 ) and ( 0.5 ) are terminating decimals.<\/p>\n\n\n\n Non-Terminating Decimal<\/strong>: A decimal is non-terminating if it continues indefinitely without repeating. An example of this is ( \\pi ) or ( e ).<\/p>\n\n\n\n Repeating Decimal<\/strong>: A decimal is termed repeating if it has a specific sequence of digits that recurs indefinitely. An example of a repeating decimal is ( 0.333\u2026 ), which can be expressed as ( \\frac{1}{3} ).<\/p>\n\n\n\n Now, let\u2019s analyze the fraction ( \\frac{3}{10} ). When we convert this fraction into a decimal:<\/p>\n\n\n\n [ The decimal ( 0.3 ) is a terminating decimal because it has a finite number of digits (only one digit after the decimal point). Therefore, it does not continue indefinitely nor does it repeat.<\/p>\n\n\n\n To further clarify, a fraction can be expressed in decimal form depending on the prime factorization of its denominator. If the denominator can be expressed as ( 2^m \\times 5^n ), where ( m ) and ( n ) are non-negative integers, the fraction will result in a terminating decimal. In this case, ( 10 = 2^1 \\times 5^1 ), confirming that ( \\frac{3}{10} ) meets this criterion.<\/p>\n\n\n\n In conclusion, ( \\frac{3}{10} ) is a terminating decimal and, therefore, is not<\/strong> non-terminating or repeating. It has a specific, finite decimal representation: ( 0.3 ).<\/p>\n","protected":false},"excerpt":{"rendered":" Is 3\/10 a non terminating and repeating? The Correct Answer and Explanation is: To determine whether the fraction ( \\frac{3}{10} ) is non-terminating and repeating, we first need to understand the definitions of terminating and non-terminating decimal representations. 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\\frac{3}{10} = 0.3
]<\/p>\n\n\n\n