SOLUTION: convert these repeating decimals. 1. 99.999 42.242424 57.357357357 2.Divide this binary number 10,010,101 x1010 3. suppose that a rectangle has the length

Question 536191: convert these repeating decimals.
1. 99.999 42.242424 57.357357357
2.Divide this binary number 10,010,101 x1010
3. suppose that a rectangle has the length L and width W that happen to be whole numbers. Recall that the perimeter P of a rectangle is the sum of its sides. If you are told that P is even what can you conclude about whether L or W is even or odd?on the other hand you were told P was odd now what would you say?
Answer by fcabanski(1391) (Show Source): You can put this solution on YOUR website!
To convert a repeating decimal to a fraction

Step 1: Count the number of repeating digits. This is n.

Step 2: Set x = the decimal number you're trying to convert.

Step 3: Multiply both sides by 10^n where n - the number of repeating digits.

Step 4. Subtract the original equation from the new equation.

Step 5. Solve for x.

Step 1. there is one repeating digit (9) so n=1.

Step 2. x=99.999...

Step 3. 10^1 = 10 so 10x=999.999... (we can add as many 9's as needed on the end because it repeats.)

Step 4. 9x = 900

Step 5. x = 900/9 = 100.

It seems wrong, but the fact is .999999999... = 1. So 99.999999999... = 100 and that's 100/1 as a fraction.

42.242424 has 2 repeating digits (24). So n=3.

x=42.2424242

10^2 = 100 so it's 100x = 4224.2424242 (add as many repeating digits as necessary so when subtracting, the decimal portion is gone.)

99x = 4182

x=4182/99 = 1394/33.

57.357357 has 3 repeating digits so n=3.

x=57.357357 and 10^3 times that is 1000x=57357.357357

999x = 57300 ---> x=57300/99=19100/33

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.

You can also divide by converting to base 10, then converting the answer back to binary.

Remember, for binary the places to the left of 0 are 2^0, 2^1, 2^2, etc.

10,010,101 = (reading from the right) 1*1+0*2+1*4+0*8+1*16+0*32+0*64+1*128 = 149

1010 is (from right) 0*1+1*2+0*4+1*8 = 10.

The problem is 149/10 = 14 R 9/10.

In binary 14 is (from right) 0*1+1*2+1*4+1*8 = 1110

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.

The answer is 1110 R 1001/1010

P=2L+2W.

If P is even then L and W could be both odd, both even, or one odd and one even.

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.

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.)

We can't tell anything about L and W as far as being even or odd just by knowing the P is even.

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.

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