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Addition and Subtraction of Decimal Numbers

If you want to add up or subtract decimal numbers you can use the same techniques used to add up or subtract integers.

You only need to pay attention to the position of the decimal mark.

Addition of decimal numbers

There are multiple methods to add up decimal numbers. You can either:

  • Write the figures underneath each other and use written addition.

  • Or convert them into fractions and add them up this way.

Procedure

Description

Calculations

Write the figures underneath each other so that the decimal marks are directly beneath each other. If the figures contain a different amount of decimal places you need to fill up the shorter number with zeros until they both have the same number of decimal places.

+6.256+2.73\phantom{+}6.256 \\+2.73

Add up the numbers without paying attention to the decimal marks (points). Then place the point of the solution directly underneath the other points.

+  6.256+  2.730\def\arraystretch{1.25} \begin{array}{l}\hphantom{ +\; } 6.256\\+\;2.730\\\end{array}

In the result, place the point directly below the other decimal marks.

+  6.256+  2.730‾+  8.986\def\arraystretch{1.25} \begin{array}{l}\hphantom{ +\; } 6.256\\\underline{+\;2.730}\\\hphantom{ +\; }8.986\end{array}

Remember

Place "point over point"

Procedure using conversion to fractions

Instead of calculating directly with decimal numbers, you can also convert them into fractions and then add them.

This method is mainly used for periodic fractions.

Subtraction of decimal numbers

As with the addition of decimal numbers, there are two different approaches you can use. You can either:

  • Write them underneath each other and use written subtraction.

  • Or convert them to fractions and subtract them.

Procedure

Description

Calculations

Write the figures underneath each other so that the decimal marks are directly beneath each other. If the figures contain a different amount of decimal places you need to fill up the shorter number with zeros until they both have the same number of decimal places.

−6.623−4.71\phantom{-}6.623\\-4.71

Use written subtraction without paying attention to the decimal marks. Then place the decimal mark of the solution directly underneath the others.

−  6.623−  4.710\def\arraystretch{1.25} \begin{array}{l}\hphantom{ -\; } 6.623\\-\;4.710\\\end{array}

In the result, the decimal mark is now placed directly below the others.

−  6̸5.6̸16  2  3−    4.  7  1  0‾−    1.  9  1  3\def\arraystretch{1.25} \begin{array}{l}\hphantom{ -\; } \overset{5}{\not6}.\overset{16}{\not6}\;2\;3\\\underline{-\;\;4.\;7\;1\;0}\\\hphantom{-\;}\;1.\;9\;1\;3\end{array}

Exercises: Addition and Subtraction of Decimal Numbers

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