# Long decimal Division

## Decimal division of two whole numbers

We show step by step how to divide two whole numbers to get a decimal quotient with a given precision.

We'll divide 6734 by 56 with a precision of 2 decimals e.g. the quotient will have two decimals.

• We start by multiplying the dividend by 10^{precision} = 10^{2} = 100. The division changes to,

673400 ÷ 56

5 | 6 | 6 | 7 | 3 | 4 | 0 | 0 |

• During the process, we'll perform successive Euclidean divisions by 56 (divisor) starting with the left digit of the dividend and continue with the remainders to which we successively add the digits of the dividend. This gives in detail,

• 6 divided by 56 equals 0 remainder 6

put 0 in the quotient

0 | |||||||

5 | 6 | 6 | 7 | 3 | 4 | 0 | 0 |

6 | |||||||

- | 0 | ||||||

6 |

• 67 divided by 56 equals 1 remainder 11.

Put 1 in the quotient.

0 | 1 | ||||||

5 | 6 | 6 | 7 | 3 | 4 | 0 | 0 |

6 | |||||||

- | 0 | ||||||

6 | 7 | ||||||

- | 5 | 6 | |||||

1 | 1 |

• 113 divided by 56 equals 2 remainder 1

Put 2 in the quotient

0 | 1 | 2 | |||||

5 | 6 | 6 | 7 | 3 | 4 | 0 | 0 |

6 | |||||||

- | 0 | ||||||

6 | 7 | ||||||

- | 5 | 6 | |||||

1 | 1 | 3 | |||||

- | 1 | 1 | 2 | ||||

1 |

• 14 divided by 56 = 0 remainder 14

Put 0 in the quotient

0 | 1 | 2 | 0 | ||||

5 | 6 | 6 | 7 | 3 | 4 | 0 | 0 |

6 | |||||||

- | 0 | ||||||

6 | 7 | ||||||

- | 5 | 6 | |||||

1 | 1 | 3 | |||||

- | 1 | 1 | 2 | ||||

1 | 4 | ||||||

- | 0 | ||||||

1 | 4 |

• 140 divided by 56 equals 2 remainder 28.

Put 2 in the quotient.

0 | 1 | 2 | 0 | 2 | |||

5 | 6 | 6 | 7 | 3 | 4 | 0 | 0 |

6 | |||||||

- | 0 | ||||||

6 | 7 | ||||||

- | 5 | 6 | |||||

1 | 1 | 3 | |||||

- | 1 | 1 | 2 | ||||

1 | 4 | ||||||

- | 0 | ||||||

1 | 4 | 0 | |||||

- | 1 | 1 | 2 | ||||

2 | 8 |

• Fianlly, 280 divided by 56 equals 5 remainder 0

Put 5 in the quotient.

0 | 1 | 2 | 0 | 2 | 5 | ||

5 | 6 | 6 | 7 | 3 | 4 | 0 | 0 |

6 | |||||||

- | 0 | ||||||

6 | 7 | ||||||

- | 5 | 6 | |||||

1 | 1 | 3 | |||||

- | 1 | 1 | 2 | ||||

1 | 4 | ||||||

- | 0 | ||||||

1 | 4 | 0 | |||||

- | 1 | 1 | 2 | ||||

2 | 8 | 0 | |||||

- | 2 | 8 | 0 | ||||

0 |

• We've multiplied the dividend by 100, so we divide the result by 100.

12025 divided by 100 = 120.25

## Division of two decimal numbers

We'll divide 4326.5 by 23.65 with a pecision of 2 decimals.

• To get whole numbers, multiply the dividend and the diviser by 100.

4326.5 × 100 = 432650

23.65 × 100 = 2365

The division changes to 432650 ÷ 2365

We then use the method described above, that applies for whole numbers.

Thus, multiply the dividend by 100 to get a precision of 2 decimals.

Perform the euclidean division of 43265000 divided by 2365 by following the steps above. We get,

0 | 0 | 0 | 1 | 8 | 2 | 9 | 3 | ||||

2 | 3 | 6 | 5 | 4 | 3 | 2 | 6 | 5 | 0 | 0 | 0 |

4 | |||||||||||

- | 0 | ||||||||||

4 | 3 | ||||||||||

- | 0 | ||||||||||

4 | 3 | 2 | |||||||||

- | 0 | ||||||||||

4 | 3 | 2 | 6 | ||||||||

- | 2 | 3 | 6 | 5 | |||||||

1 | 9 | 6 | 1 | 5 | |||||||

- | 1 | 8 | 9 | 2 | 0 | ||||||

6 | 9 | 5 | 0 | ||||||||

- | 4 | 7 | 3 | 0 | |||||||

2 | 2 | 2 | 0 | 0 | |||||||

- | 2 | 1 | 2 | 8 | 5 | ||||||

9 | 1 | 5 | 0 | ||||||||

- | 7 | 0 | 9 | 5 | |||||||

2 | 0 | 5 | 5 |

• Divide the result by 100,

We get the final result 182.93.

## See also

Long Addition

Long Subtraction

Long Multiplication

Long Euclidian Division