document.write( "Question 328145: a. Separate the fractions 2/6, 2/5, 6/13, 1/25, 7/8, and 9/29 into two
\n" ); document.write( "categories: those that can be written as a terminating
\n" ); document.write( "decimal and those that cannot. Write an explanation
\n" ); document.write( "of how you made your decisions.
\n" ); document.write( "b. Form a conjecture about which fractions can be
\n" ); document.write( "expressed as terminating decimals.
\n" ); document.write( "c. Test your conjecture on the following fractions:6/12, 7/15, 28/140,
\n" ); document.write( "and 0/7
\n" ); document.write( "d. Use the ideas of equivalent fractions and common
\n" ); document.write( "multiples to verify your conjecture.\r
\n" ); document.write( "\n" ); document.write( "I thought that I had part A but then I did not understand B, C, and D. Please help me, thank you so much:) \n" ); document.write( "
Algebra.Com's Answer #235038 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
a. Separate the fractions 2/6, 2/5, 6/13, 1/25, 7/8, and 9/29 into two
\n" ); document.write( "categories: those that can be written as a terminating
\n" ); document.write( "decimal and those that cannot.
\n" ); document.write( "
\r\n" );
document.write( "2/6 = 1/3 = 0.333333333333333333333333333333333333333333333333333..., no \r\n" );
document.write( "2/5 = 0.4, yes, a terminating decimal\r\n" );
document.write( "6/13 = 0.461538461538461538461538461538461538461538461538461538..., no\r\n" );
document.write( "1/25 = 0.04, yes, a terminating decimal\r\n" );
document.write( "7/8 = 0.975, yes, a terminating decimal\r\n" );
document.write( "9/29 = 0.310344827586290689655172..., no\r\n" );
document.write( "\r\n" );
document.write( "Write an explanation\r\n" );
document.write( "of how you made your decisions.\r\n" );
document.write( "\r\n" );
document.write( "First we reduce the proper fractions to their lowest terms.  \r\n" );
document.write( "That only involved reducing 2/6 to 1/3.\r\n" );
document.write( "\r\n" );
document.write( "The only prime factors of denominators 3, 5, 25, and 8 are 2 and 5.\r\n" );
document.write( "The denominators 6, 13, and 29 have other prime factors besides 2 and 5. \r\n" );
document.write( " \r\n" );
document.write( "\r\n" );
document.write( "b. Form a conjecture about which fractions can be\r\n" );
document.write( "expressed as terminating decimals.\r\n" );
document.write( "\r\n" );
document.write( "If the only prime factors of the denominator of a non-zero common fraction,\r\n" );
document.write( "when reduced to lowest terms are 2 and 5, then the fraction can be written\r\n" );
document.write( "as a terminating decimal, otherwise it can only be written as a \r\n" );
document.write( "repeating decimal. \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "c. Test your conjecture on the following fractions:6/12, 7/15, 28/140,\r\n" );
document.write( "and 0/7\r\n" );
document.write( "\r\n" );
document.write( "6/12 reduces to 1/2, and the denominator has no prime factor other\r\n" );
document.write( "than 2 or 5.  In fact it has only prime factor 2.  So it can be\r\n" );
document.write( "expressed as the terminating decimal .5 \r\n" );
document.write( "\r\n" );
document.write( "7/15 is already in lowest terms, but its denominator contains prime\r\n" );
document.write( "factor 3, so its denominator does not have only prime factors 2 and 5.\r\n" );
document.write( "So 7/15 cannot be expressed as a terminating decimal, but only the\r\n" );
document.write( "repeating decimal .466666666666666666666666666...\r\n" );
document.write( "\r\n" );
document.write( "28/140 reduces to 1/5, and the denominator has no prime factor other\r\n" );
document.write( "than 2 or 5.  In fact it has only prime factor 5.  So it can be\r\n" );
document.write( "expressed as the terminating decimal .2\r\n" );
document.write( "\r\n" );
document.write( "0/7 That fraction equals 0, so it cannot be expressed as a\r\n" );
document.write( "terminating decimal.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "d. Use the ideas of equivalent fractions and common\r\n" );
document.write( "multiples to verify your conjecture.\r\n" );
document.write( "\r\n" );
document.write( "Any terminating decimal < 1 which has n digits can be written as\r\n" );
document.write( "a fraction which has those n digits as a numerator and 10^n as\r\n" );
document.write( "a denominator. 10^n has only 2 and 5 as prime factors, and if\r\n" );
document.write( "the fraction is reducted to lowest terms, its denominator still \r\n" );
document.write( "will not have any prime factors other than 2 and 5.  \r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" ); document.write( "
\n" );