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How to Do Long Division With Decimals (Mathematics Lesson)

What Is Long Division?

Long division is a method for dividing numbers.

It is possible to use long division to divide into a decimal, divide by a decimal, and both together.

How to Divide Into a Decimal

Long division can be used when the dividend is a decimal.

Question: What is the answer to the division below?:



  • Identify the dividend and the divisor:



  • Write the dividend and divisor as follows:



  • Divide the first digit of the dividend (8) by the divisor (4), and write the whole number answer above the line. (Note: do not count remainders.)
    8 ÷ 4 = 2.



  • Multiply the answer from the previous operation (2) with the divisor (4). Write the result underneath the number divided into.
    2 × 4 = 8.



  • Subtract the bottom number from the top number.
    8 - 8 = 0.


  • The decimal point has been reached.

    Place a decimal point in the answer, directly above the decimal point in the dividend.


  • With the decimal point dealt with, long division carries on as normal.

    Bring down the next digit of the dividend (4).



  • Divide this number (4) by the divisor (4), and write the whole number answer above the line. (Note: do not count remainders.)
    4 ÷ 4 = 1.

There are no more digits to bring down.

The solution to 8.4 ÷ 4 is 2.1.

How To Divide By a Decimal

Long division can be used when the divisor is a decimal.

Question: What is the answer to the division below?:



  • Identify the dividend and the divisor.



  • Count how many digits there are after the decimal point in the divisor.
    There is 1 digit after the decimal point:



  • To do the division, we want the divisor to be a whole number. Move the decimal point to the right as many places to make it a whole number.

    There was 1 digit after the decimal place, so move the decimal point 1 place to the right:



    To keep the division the same, move the decimal point the same number of places to the right in the dividend.

    Move the decimal place in the dividend 1 place to the right:



    The division has become:



  • Write the dividend and divisor as follows:



  • Divide the first digit of the dividend (4) by the divisor (2), and write the whole number answer above the line. (Note: do not count remainders.)
    4 ÷ 2 = 2.



  • Multiply the answer from the previous operation (2) the divisor (2). Write the result underneath the number divided into.
    2 × 2 = 4.



  • Subtract the bottom number from the top number.
    4 - 4 = 0.



  • Bring down the next digit of the dividend (0).



  • Divide this number (0) by the divisor (2), and write the whole number answer above the line. (Note: do not count remainders.)
    0 ÷ 2 = 0.


All the digits have been brought down.

The solution to 4 ÷ 0.2 is 20.

How To Divide When Both Numbers Are Decimals

The slider below shows an example of how to do long division, when both dividend and divisor are decimals:
Interactive Test
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Note

PARTS OF A DIVISION



  • The number you divide is the dividend.

  • The number you divide by is the divisor.

  • The result of the division is the quotient.

DIVISION AS THE OPPOSITE OF MULTIPLICATION

Division is the opposite, or inverse, of multiplication.

If:



then:



and:



If two factors multiply to a product, then the product divides by one factor to the other factor.

Top Tip

DIVIDING INTO A DECIMAL

Dividing into a decimal is much like normal long division - just put a decimal point in the answer directly above the decimal point within the dividend.



ZEROES AFTER THE DECIMAL POINT

In long division, digits of the dividend often have to be bought down.

Remember that after the last digit after a decimal point, there are endless number of 0s:



It may be that one of these 0s will have to be bought down in a long division.