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To convert a repeating decimal to a fraction
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document.write( "Step 1: Count the number of repeating digits. This is n.
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document.write( "Step 2: Set x = the decimal number you're trying to convert.
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document.write( "Step 3: Multiply both sides by 10^n where n - the number of repeating digits.
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document.write( "Step 4. Subtract the original equation from the new equation.
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document.write( "Step 5. Solve for x.
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document.write( "Step 1. there is one repeating digit (9) so n=1.
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document.write( "Step 2. x=99.999...
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document.write( "Step 3. 10^1 = 10 so 10x=999.999... (we can add as many 9's as needed on the end because it repeats.)
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document.write( "Step 4. 9x = 900
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document.write( "Step 5. x = 900/9 = 100.
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document.write( "It seems wrong, but the fact is .999999999... = 1. So 99.999999999... = 100 and that's 100/1 as a fraction.
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document.write( "42.242424 has 2 repeating digits (24). So n=3.
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document.write( "x=42.2424242
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document.write( "10^2 = 100 so it's 100x = 4224.2424242 (add as many repeating digits as necessary so when subtracting, the decimal portion is gone.)
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document.write( "99x = 4182
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document.write( "x=4182/99 = 1394/33.
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document.write( "57.357357 has 3 repeating digits so n=3.
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document.write( "x=57.357357 and 10^3 times that is 1000x=57357.357357
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document.write( "999x = 57300 ---> x=57300/99=19100/33
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document.write( "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.
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document.write( "You can also divide by converting to base 10, then converting the answer back to binary.
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document.write( "Remember, for binary the places to the left of 0 are 2^0, 2^1, 2^2, etc.
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document.write( "10,010,101 = (reading from the right) 1*1+0*2+1*4+0*8+1*16+0*32+0*64+1*128 = 149
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document.write( "1010 is (from right) 0*1+1*2+0*4+1*8 = 10.
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document.write( "The problem is 149/10 = 14 R 9/10.
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document.write( "In binary 14 is (from right) 0*1+1*2+1*4+1*8 = 1110
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document.write( "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.
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document.write( "The answer is 1110 R 1001/1010
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document.write( "P=2L+2W.
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document.write( "If P is even then L and W could be both odd, both even, or one odd and one even.
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document.write( "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.
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document.write( "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.)
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document.write( "We can't tell anything about L and W as far as being even or odd just by knowing the P is even.
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document.write( "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.\r
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document.write( "($3.50-$5.50 per problem. Contact me (check the profile \"website\" which is \r
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document.write( "my email address.
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