simplify (show your work) 
17.23/0.035 (to one decimal place) 
Thanks for the help
     ______
0.035)17.23

First we must move the decimal place in the divisor 0.035 
three places to the right to get the decimal to the right 
so we can delete it and make it just the whole number 0035,
but we drop the two 0's in the beginning and make it 35

Secondly since we moved the divisor's decimal three places
to the right, we must also move the decimal place of the
dividend 17.23 three places to the right also.  However
since there are only two places after the decimal in 17.23
we annex another 0, making it 17.230 so that we can move
the decimal three places to the right and have 17230. Since
we want to get the answer to one decimal place, we annex a
decimal and a 0 on the end of 17230, making it 17230.0

So we have
 
          
35)17230.0 

Place a decimal directly above the decimal

        . 
35)17230.0 

To get an idea of what digit to put first, we divide
the first digit 3 of 35 into the first two digits of 17230
since the first digit of 17230 is less than 3.  So 3 goes
into 17 5+ times, so we try 5:

     5  . 
35)17230.0 
   175

No, 5 is too much, because we cannot subtract 175 from 172.
So we try 1 less, or 4

     4  . 
35)17230.0 
   140
   
Now we subtract and get

     4  . 
35)17230.0 
   140
    32

Now we bring down the next digit of the dividend, 3.

     4  . 
35)17230.0 
   140
    323

Now we divide the first digit 3, of the divisor 35,
into the first two digits 32, of 323.  So we try 9

     49 . 
35)17230.0 
   140
    323

Multiply 9 times 35 and get 315. Write that under the 
323

     49 . 
35)17230.0 
   140
    323
    315 
      
Subtract 315 from 323 and get 8

     49 . 
35)17230.0 
   140
    323
    315 
      8

Bring down the next digit from
the dividend, 0.

     49 . 
35)17230.0 
   140
    323
    315 
      80

The first digit of 35, 3, goes into the first
digit of 80, which is 8,  2 times.  So we try a 2
next to the 9 in the quotient.

     492. 
35)17230.0 
   140
    323
    315 
      80
      
Then we multiply 4 by 35 and get 70 and write it
under the 80

     492. 
35)17230.0 
   140
    323
    315 
      80
      70
     
We subtract 70 from 80 and get 10 and write it at
the bottom:

     492. 
35)17230.0 
   140
    323
    315 
      80
      70
      10 

Bring down the last digit from the divisor, 0.

     492. 
35)17230.0 
   140
    323
    315 
      80
      70
      10 0

The first digit of 35, 3, divides into the first
two digits of 100, namely 10, 3 times, so we try
3 in the quotient after the decimal

     492.3
35)17230.0 
   140
    323
    315 
      80
      70
      10 0
     
Now we multiply 3 by 35 and get 105.

     492.3
35)17230.0 
   140
    323
    315 
      80
      70
      10 0
      10 5

But we cannot subtract 105 from 100, so
we try 1 less than 3, or 2.

     492.2
35)17230.0 
   140
    323
    315 
      80
      70
      10 0
       7 0
       
and subtract

     492.2
35)17230.0 
   140
    323
    315 
      80
      70
      10 0
       7 0
       3 0

Now we are done except for deciding
whether we leave the answer 492.2 or
whether we round it up to 492.3.

We round it it up to 492.3 because the
remainder 30 is at least half of the
divisor 35. So the answer is 492.3

Edwin
AnlytcPhil@aol.com