document.write( "Question 1209439: When the multiplication 5 013 698 472 × 999 999 999 is performed, what is the only digit that does not appear in the product?
\n" ); document.write( "CC12#4 \n" ); document.write( "
Algebra.Com's Answer #848831 by ikleyn(52858)\"\" \"About 
You can put this solution on YOUR website!
.
\n" ); document.write( "When the multiplication 5 013 698 472 × 999 999 999 is performed,
\n" ); document.write( "what is the only digit that does not appear in the product?
\n" ); document.write( "~~~~~~~~~~~~~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "
\r\n" );
document.write( "Let's perform the multiplication.  The product is \r\n" );
document.write( "\r\n" );
document.write( "      5 013 698 472 × 999 999 999 = 5 013 698 472 × (1 000 000 000 - 1) = \r\n" );
document.write( "\r\n" );
document.write( "    = 5 013 698 472 000 000 000 - 5 013 698 472 = \r\n" );
document.write( "\r\n" );
document.write( "      \r\n" );
document.write( "      5 013 698 472 000 000 000\r\n" );
document.write( "  -               5 013 698 472\r\n" );
document.write( "      --------------------------\r\n" );
document.write( "      5 013 698 466 986 301 528    <<<---===  the product\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The only digit which does not appear in the product is 7.\r\n" );
document.write( "
\r
\n" ); document.write( "\n" ); document.write( "Solved.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "------------------\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "This problem is probably 400 or 500 years old, if not more.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "It could have been created around the time the Arabs
\n" ); document.write( "invented the modern form of decimal notation.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "It is what Britannica says \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "
\r\n" );
document.write( "    Hindu-Arabic numerals, set of 10 symbols — 1, 2, 3, 4, 5, 6, 7, 8, 9, 0 — that represent numbers \r\n" );
document.write( "    in the decimal number system. They originated in India in the 6th or 7th century and were introduced \r\n" );
document.write( "    to Europe through the writings of Middle Eastern mathematicians, especially al-Khwarizmi and al-Kindi, \r\n" );
document.write( "    about the 12th century. \r\n" );
document.write( "
\r
\n" ); document.write( "\n" ); document.write( "It is what AI says\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "
\r\n" );
document.write( "    The Arabs did not actually invent the modern form of numeric notation, as it originated in India \r\n" );
document.write( "    and is more accurately called the \"Hindu-Arabic numeral system\"; however, they were instrumental \r\n" );
document.write( "    in spreading this system to Europe, which is why they are often associated with it; \r\n" );
document.write( "    the system reached its modern form around the 8th to 9th centuries in the Arab world, \r\n" );
document.write( "    with mathematicians like al-Khwarizmi playing a key role in its dissemination. \r\n" );
document.write( "
\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
\n" );