document.write( "Question 108912: Can someone PLEASE HELP me with this problem, I really do NOT understand any of this problem , if someone could please explain and help me with all these questions to this problem I would so much appreciate it.
\n" ); document.write( "THANK YOU!!!!
\n" ); document.write( "Every fraction has a decimal equivalent that__either terminates (for example, 1/4 = 0.25) or repeats (for example,2/9 = 0.2). (The line is above the 2 of the 0.2) Work with a group to discover which fractions have terminating decimals and which have repeating decimals. You may assume that the numerator of each fraction you consider is and focus your attention on the denominator. As you complete
\n" ); document.write( "the table below, you will find that the key to this question lies with the prime factorization of the denominator.\r
\n" ); document.write( "\n" ); document.write( " Prime Factorization
\n" ); document.write( "Fraction Decimal Form Terminate? of the Denominator _______________________________________________________________________________\r
\n" ); document.write( "\n" ); document.write( "1/2
\n" ); document.write( "1/3
\n" ); document.write( "1/4
\n" ); document.write( "1/5
\n" ); document.write( "1/6
\n" ); document.write( "1/7
\n" ); document.write( "1/8
\n" ); document.write( "1/9
\n" ); document.write( "1/10
\n" ); document.write( "1/11
\n" ); document.write( "1/12\r
\n" ); document.write( "\n" ); document.write( "State a general rule describing which fractions have decimal forms that terminate andwhich have decimal forms that repeat.
\n" ); document.write( "Now test your rule on at least three new fractions. That is, be able to predict whether a fraction such as 1/25 or 1/30 has a terminating decimal or a repeating decimal. Then confirm your prediction. \n" ); document.write( "
Algebra.Com's Answer #79473 by Edwin McCravy(20054)\"\" \"About 
You can put this solution on YOUR website!
Can someone PLEASE HELP me with this problem, I really do NOT understand any of this problem , if someone could please explain and help me with all these questions to this problem I would so much appreciate it.
\n" ); document.write( "THANK YOU!!!!
\n" ); document.write( "Every fraction has a decimal equivalent that__either terminates (for example, 1/4 = 0.25) or repeats (for example,2/9 = 0.2). (The line is above the 2 of the 0.2) Work with a group to discover which fractions have terminating decimals and which have repeating decimals. You may assume that the numerator of each fraction you consider is 1 and focus your attention on the denominator. As you complete the table below, you will find that the key to this question lies with the prime factorization of the denominator.
\n" ); document.write( "Prime Factorization
\n" ); document.write( "Fraction Decimal Form Terminate? of the Denominator
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document.write( "_______________________________________________________________________________ \r\n" );
document.write( "1/2 = .5 so it is terminating\r\n" );
document.write( "1/3 = .33333··· so it is repeating\r\n" );
document.write( "1/4 = .25 so it is terminating\r\n" );
document.write( "1/5 = .2 so it is terminating\r\n" );
document.write( "1/6 = .166666··· so it is repeating\r\n" );
document.write( "1/7 = .142857142857142857··· so it is repeating\r\n" );
document.write( "1/8 = .125 so it is terminating\r\n" );
document.write( "1/9 = .11111··· so it is repeating\r\n" );
document.write( "1/10 = .1 so it is terminating\r\n" );
document.write( "1/11 = .09090909··· so it is repeating\r\n" );
document.write( "1/12  = .0833333··· so it is repeating\r\n" );
document.write( "

\n" ); document.write( "State a general rule describing which fractions have
\n" ); document.write( "decimal forms that terminate and which have decimal forms
\n" ); document.write( "that repeat.
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\r\n" );
document.write( "The denominators of the fractions above whose decimal form\r\n" );
document.write( "terminates are 2, 4, 5, 8, and 10.  Each of these either has\r\n" );
document.write( "prime factors 2 and/or 5, and ONLY those.\r\n" );
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document.write( "The denominators of the fractions above whose decimal form\r\n" );
document.write( "is repeating are 3, 6, 7, 9, and 11.  These all have at least \r\n" );
document.write( "one prime factor which is neither 2 nor 5.\r\n" );
document.write( " \r\n" );
document.write( "General rule:  If the denominator of a common fraction which is\r\n" );
document.write( "in lowest terms has no prime factor other than 2 or 5, its decimal \r\n" );
document.write( "form terminates.\r\n" );
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document.write( "If the denominator of a common fraction which is in lowest terms\r\n" );
document.write( "has any prime factor other than 2 or 5, its decimal form is a \r\n" );
document.write( "repeating decimal.\r\n" );
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document.write( "Now test your rule on at least three new fractions. That is, be \r\n" );
document.write( "able to predict whether a fraction such as 1/25 or 1/30 has a \r\n" );
document.write( "terminating decimal or a repeating decimal. Then confirm your \r\n" );
document.write( "prediction.\r\n" );
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document.write( "The denominator of 1/25 is 25, and 25 has no other prime factor\r\n" );
document.write( "but 5, so its decimal form terminates as .04\r\n" );
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document.write( "The denominator of 1/30 is 30, and 30 has the prime factor 3\r\n" );
document.write( "which is neither 2 nor 5, so its decimal form is the repeating decimal .033333···\r\n" );
document.write( "\r\n" );
document.write( "The denominator of 3/16 is 16, and 16 has no prime factor other\r\n" );
document.write( "than 2, so its decimal form terminates as .1875.\r\n" );
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document.write( "The denominator of 5/26 is 26, and 26 has the prime factor 13\r\n" );
document.write( "but 5, so its decimal form is the repeating decimal \r\n" );
document.write( ".1923076923076923076···\r\n" );
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document.write( "The denominator of 119/125 is 125, and 125 has no prime factor other\r\n" );
document.write( "than 5, so its decimal form terminates as .952.\r\n" );
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document.write( "The denominator of 17/28 is 28, and 28 has the prime factor 7\r\n" );
document.write( "which is neither 2 nor 5, so its decimal form is the repeating \r\n" );
document.write( "decimal .60714285714285714285···\r\n" );
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document.write( "Edwn
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