<PRE><B>Question 536191</B>
To convert a repeating decimal to a fraction&lt;P&gt;
Step 1:  Count the number of repeating digits.  This is n.&lt;P&gt;
Step 2:  Set x = the decimal number you&#39;re trying to convert.&lt;P&gt;
Step 3:  Multiply both sides by 10^n where n - the number of repeating digits.&lt;P&gt;
Step 4.  Subtract the original equation from the new equation.&lt;P&gt;
Step 5.  Solve for x.&lt;P&gt;

Step 1.  there is one repeating digit (9) so n=1.  &lt;P&gt;
Step 2. x=99.999...&lt;P&gt;
Step 3. 10^1 = 10 so 10x=999.999...  (we can add as many 9&#39;s as needed on the end because it repeats.)&lt;P&gt;
Step 4.  9x = 900&lt;P&gt;
Step 5.  x = 900/9 = 100.&lt;P&gt;
It seems wrong, but the fact is .999999999... = 1.  So 99.999999999... = 100 and that&#39;s 100/1 as a fraction.&lt;P&gt;
42.242424 has 2 repeating digits (24).  So n=3. &lt;P&gt;
x=42.2424242 &lt;P&gt;
10^2 = 100 so it&#39;s 100x = 4224.2424242 (add as many repeating digits as necessary so when subtracting, the decimal portion is gone.)&lt;P&gt;
99x = 4182&lt;P&gt;
x=4182/99 = 1394/33.&lt;P&gt;
57.357357 has 3 repeating digits so n=3.&lt;P&gt;
x=57.357357 and 10^3 times that is 1000x=57357.357357&lt;P&gt;
999x = 57300 ---&gt; x=57300/99=19100/33&lt;P&gt;
I have no idea how to write out the binary division here.  If you email (send a thank you which will then send me your email address) I will send an image of that binary division solved.&lt;P&gt;
You can also divide by converting to base 10, then converting the answer back to binary.&lt;P&gt;

Remember, for binary the places to the left of 0 are 2^0, 2^1, 2^2, etc.&lt;P&gt;
10,010,101 = (reading from the right) 1*1+0*2+1*4+0*8+1*16+0*32+0*64+1*128 = 149&lt;P&gt;
1010 is (from right) 0*1+1*2+0*4+1*8 = 10.&lt;P&gt;
The problem is 149/10 = 14 R 9/10. &lt;P&gt;
In binary 14 is (from right) 0*1+1*2+1*4+1*8 = 1110&lt;P&gt;
9 is (from right) 1*1+0*2+0*4+1*8 = 1001 and 10 is (from right) 0*1+1*2+0*4+1*8=1010.&lt;P&gt;
The answer is 1110 R 1001/1010&lt;P&gt;
P=2L+2W.&lt;P&gt;
If P is even then L and W could be both odd, both even, or one odd and one even.&lt;P&gt;
P = 26 = 2L+2W and 26/2=13 = L+W so if one is even the other is odd.  (12+1, or 11+2, or 10+3, or 9+4 etc.).  Also note that either the length or width can be odd, and the other even.&lt;P&gt;
P=32 =2L+2W and 16=L+W.  Both L and W can be even, or both can be odd.  (9+7=16, 10+6=16.)&lt;P&gt;
We can&#39;t tell anything about L and W as far as being even or odd just by knowing the P is even.&lt;P&gt;
The second case, P being odd, is not possible.  P = 2L +2W.  2 times an even number is even and 2 times an odd number is even and even + even is always even.

&lt;P&gt;&lt;B&gt;I provide online tutoring ($30/hr) and personal problem solving 

($3.50-$5.50 per problem.  Contact me (check the profile &quot;website&quot; which is 

my email address.&lt;/B&gt;&lt;P&gt;


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