document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1122513>Question 1122513</A>: <I><SPAN STYLE=\"word-break: break-all;\"> express the foloowing recurring decimals as an infinite G.P. and then find out their values as a rational number. the *x* refer to the recurring part<BR>\n" );
document.write( "(a)0.*7* <BR>\n" );
document.write( "(b)0.3*15*                              </SPAN>\n" );
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document.write( "(a) x = 0.*7* = 7/10 + 7/100 + 7/1000 + ...<br><BR>\n" );
document.write( "This is a geometric progression with first term 7/10 and common ratio 1/10; the infinite sum is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%287%2F10%29%2F%281-%281%2F10%29%29+=+%287%2F10%29%2F%289%2F10%29+=+7%2F9 ALIGN=MIDDLE  ALT=\"%287%2F10%29%2F%281-%281%2F10%29%29+=+%287%2F10%29%2F%289%2F10%29+=+7%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Answer: 0.*7* = 7/9<br><BR>\n" );
document.write( "(b) x = 0.3*15* = 3/10 + 15/1000 + 15/100000 + 15/10000000 + ...<br><BR>\n" );
document.write( "After the first term, the rest is a geometric progression with first term 15/1000 and common ratio 1/100; its infinite sum is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2815%2F1000%29%2F%281-%281%2F100%29%29+=++%2815%2F1000%29%2F%2899%2F100%29+=+%2815%2F1000%29%2F%28990%2F1000%29+=+15%2F990 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Then the entire decimal number is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F10+%2B+15%2F990+=+297%2F990+%2B+15%2F990+=+312%2F990 ALIGN=MIDDLE  ALT=\"3%2F10+%2B+15%2F990+=+297%2F990+%2B+15%2F990+=+312%2F990\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Answer: 0.3*15* = 312/990; simplify if required. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );