document.write( "Question 545299: 1. Convert the binary number 111,000,111 into the base ten equivalent.\r
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document.write( "2. Convert the base ten number 111 into the binary equivalent.\r
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document.write( "3. Convert the decimal number 0.35743574357435743574357435743574 to a fraction \n" );
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Algebra.Com's Answer #355552 by Edwin McCravy(20055)![]() ![]() You can put this solution on YOUR website! 1. Convert the binary number 111000111 into the base ten equivalent. \n" ); document.write( " \r\n" ); document.write( " 1 1 1 0 0 0 1 1 1 \r\n" ); document.write( "\r\n" ); document.write( "1*28 + 1*27 + 1*26 + 0*25 + 0*24 + 0*23 + 1*22 + 1*21 + 1*20\r\n" ); document.write( " 258 + 128 + 64 + 0 + 0 + 0 + 4 + 2 + 1 = 457\r\n" ); document.write( " \n" ); document.write( "2. Convert the base ten number 111 into the binary equivalent. \n" ); document.write( " \r\n" ); document.write( "\r\n" ); document.write( "Keep dividing by 2 putting the quotients underneath and the\r\n" ); document.write( "remainder out to the right beside the quotient. Quit when\r\n" ); document.write( "the quotient becoms 0. Then the digits of the binary number\r\n" ); document.write( "are the remainders reading from bottom to top:\r\n" ); document.write( "\r\n" ); document.write( " 2)111\r\n" ); document.write( " 2)55 1\r\n" ); document.write( " 2)27 1\r\n" ); document.write( " 2)13 1\r\n" ); document.write( " 2)6 0\r\n" ); document.write( " 2)3 1\r\n" ); document.write( " 2)1 1\r\n" ); document.write( " 0 1 \r\n" ); document.write( " \r\n" ); document.write( "List the remainders from bottom to top\r\n" ); document.write( "\r\n" ); document.write( "Answer: 1110111 \r\n" ); document.write( "\r\n" ); document.write( "\r\n" ); document.write( "3. Convert the decimal number 0.35743574357435743574357435743574...\r\n" ); document.write( " to a fraction\r\n" ); document.write( "\r\n" ); document.write( " N = 0.35743574357435743574357435743574...\r\n" ); document.write( "\r\n" ); document.write( "There are four repeating digits so multiply both sides by 10410> or 10000\r\n" ); document.write( "\r\n" ); document.write( " 10000N = 3574.3574357435743574357435743574...\r\n" ); document.write( "\r\n" ); document.write( "Subtract the original equation for N\r\n" ); document.write( "\r\n" ); document.write( " 10000N = 3574.35743574357435743574357435743574...\r\n" ); document.write( " N = 0.35743574357435743574357435743574...\r\n" ); document.write( "--------------------------------------------------\r\n" ); document.write( " 9999N = 3574\r\n" ); document.write( "\r\n" ); document.write( " N =\n" ); document.write( " |