# Long addition

## Long Addition with Whole Numbers

We show in steps how to add whole numbers (ie "without decimals") using this example 454 + 782.

• Start by stacking the numbers to add and aligning them to the right. So, the digits of the ones (4 and 2) are in the same (first) column, the digits of tens (5 and 8) are in the same (second) column and so on.

4 | 5 | 4 | |

+ | 7 | 8 | 2 |

= |

• We add the digits of the same column starting with the right column (column of ones) and put the result in the bottom of the same column.

4 + 2 = **6**

4 | 5 | 4 | |

+ | 7 | 8 | 2 |

= | 6 |

• We continue with the 2nd column (tens place).

5 + 8 = 1**3**

This time the result has 2 digits: we put the ones digit (=3) in the result (bottom of the 2nd column) and we carry the tens digit (=1) to the next column (=3rd column).

1 | |||

4 | 5 | 4 | |

+ | 7 | 8 | 2 |

= | 3 | 6 |

• We continue with the 3rd column (hundreds). We add the digits including the carry from the previous step.

1 + 4 + 7 = **12**

Since this is the last column: we put the result "as is", i.e. whatever the number of its digits.

1 | ||||

4 | 5 | 4 | ||

+ | 7 | 8 | 2 | |

= | 1 | 2 | 3 | 6 |

## Long addition of decimal numbers

We show the steps for the following long addition 12.4547 + 3.82 + 878.874

• Start by stacking the numbers to be added and aligning them from the decimal separator. The decimal separators must be aligned in the same column.

1 | 2 | . | 4 | 5 | 4 | 7 | ||

+ | 3 | . | 8 | 2 | ||||

+ | 8 | 7 | 8 | . | 8 | 7 | 4 | |

= |

• Fill the blank places after the decimal separator with zeros.

1 | 2 | . | 4 | 5 | 4 | 7 | ||

+ | 3 | . | 8 | 2 | 0 | 0 | ||

+ | 8 | 7 | 8 | . | 8 | 7 | 4 | 0 |

= |

• We proceed exactly as in the previous case with whole numbers (see 1st paragraph for more details).

The long addition is as follows,

1 | 2 | 1 | ||||||

1 | 2 | . | 4 | 5 | 4 | 7 | ||

+ | 3 | . | 8 | 2 | 0 | 0 | ||

+ | 8 | 7 | 8 | . | 8 | 7 | 4 | 0 |

= | 8 | 9 | 5 | . | 1 | 4 | 8 | 7 |

**1st column**

7 + 0 + 0 = 7

We put 7 in the result.

**2nd column**

4 + 0 + 4 = 4

We put 4 in the result.

**3rd column**

5 + 2 + 7 = 14

We put 4 and carry 1.

**4th column**

1 (carry) + 4 + 8 + 8 = 21

We put 1 and carry 2.

**5th column**

Column of decimal separators that we keep in the result.

**6th column**

2 (carry) + 2 + 3 + 8 = 15

We put 5 and carry 1.

**7th column**

1 (carry) + 1 + 7 = 9

We put 9 in the result.

**8th column**

We put 8 (the only digit in the column) in the result.

## See also

Long Subtraction

Long Multiplication Calculator

Long decimal Division

Long Euclidean Division Calculator

Big numbers Calculator

Number Calculators

Mathematics Calculators