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How to Divide Decimals Step by Step

Division along with addition, subtraction and multiplication form the four basic arithmetic operations. Dividing decimals is done using methods similar to methods that are used for dividing integers.The long division used for dividing numbers are used for dividing decimals as well adding steps that are needed specially for decimals. The steps involved can be enumerated as follows:
  1. If the divisor ( the number that divides) is a decimal, convert that to an integer by suitable multiplication.
  2. Multiply the dividend (the number that is being divided) also by the same number, which is used in step 1.
  3. If the dividend do not contain a decimal point add a decimal point at the right end and append a zero.
  4. Do the long division as done for integers.
  5. Division is complete when the remainder = 0
  6. If the division does not yield 0 remainder, continue division till you get the required number of decimal digits in the quotient.

How to do long division step-by-step An example

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Find $1.296\div 0.16%
Both the dividend 1.296 and the divisor 0.16 are decimals here.
Step 1:  Multiplication of decimals
As there are two decimal digits in 0.16, we need to multiply it by 100 to get rid of the decimal
Multiply each decimal by 100
0.16 x 100 =16
1.296 x 100 = 129.6


Step 2 : Beginning Long division
        8          ←    8 is written as the quotient. ( Note the quotient is written directly above the last digit taken for division.
16)129.6
     128         ← 8 x 16 = 128
    --------
         1
Step 3:  We are on the decimal place. Place  the decimal point in the quotient.
        8.         ← Decimal placed just above the decimal point in the dividend.
16)129.6
     128
     --------
         1
Step: 4 Continue long division bringing the next digit down
        8.1      ← 1 is appended to the quotient.
16)129.6
     128 ↓
     ------↓--
         1      ← The next digit is brought down.
         16       ← 1 x 16 = 16
     ----------
           0       ← No more digits to bring down and remainder =0. The division is complete.

Hence  $1.296\div 0.16%= 8.1

Decimal division and rounding

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Find $865.72\div 2.52$  round the answer to the nearest tenth.
Here we need to continue division till we get a digit in the hundredth place of the quotient.
To remove decimals from 2.52 we need to multiply by 100.
2.52 x 100 = 252
865.72 x100 = 86572

So we need to divide 86572 by 252.

          343.53
252)86572.0      ←A decimal and 0 annexed to the dividend
      756↓↓ ↓      ← We can estimate 3 as the quotient here as 3 x 25 =75  and we get 3 x 252 = 756
     ------↓↓-↓---
      1097↓ ↓       ← The next digit 7 is brought down
      1008↓ ↓       ← Again roughly 4 is the quotient  4 x 252 = 1008
    ---------↓-↓--
         892 ↓        ←  The next digit 2 is brought down.
         756 ↓
   ------------↓---
         1360          ← The decimal has started. Decimal point added to the quotient and 0 appended here for further division.
         1260          ← 5 x 252 = 1260. 5 is appended to the quotient.
   ------------------
           1000        ← One more decimal digit is needed for the quotient. 0 appended for continuing division.
             756        ← 3 x 252 = 756.  3 is appended to the quotient.
     ----------------
             244        ← We stop division here, as we have a digit in the hundredth's place of the quotient.
Since the digit in hundredth' s place is 3 which is less than 5, the quotient is rounded as 343.5
$865.72\div 2.52$ = 343.5  rounded to the tenth.