Adding Decimals

Adding decimals is very similar to adding integers (more detailed examples in adding whole numbers note) except for only one key difference: you need to line up decimals (write dots one under another) before adding.

Example 1. Calculate `6.2+1.3`.

Line up decimals and perform addition:

$$$\begin{compactarray}\ &6&\color{red}{.}&2\\+&1&\color{red}{.}&3 \\ \hline&7&\color{red}{.}&5 \end{compactarray}$$$

So, 6.2+1.3=7.5.

Sometimes number of digits can be different, so we need to pad number with zeros.

Example 2. Calculate `34.2+12.57`.

Line up decimals and pad number 34.2 with zero:

$$$\begin{compactarray}\ & 34&\color{red}{.}&2\color{green}{0} \\ + & 12& \color{red}{.}&57 \\ \hline & 46&\color{red}{.}&77 \\ \end{compactarray}$$$

So, 34.2+12.57=46.77.

Sometimes, we need to add zeros in front of number as well!

This example also involves adding positive and negative numbers.

Example 3. Calculate `15.2+(-3.432)`.

Line up decimals, pad first number with two zeros and add one zero in front of the second number.

Also, don't forget that adding negative number is actually subtracting positive.

$$$\begin{compactarray} \ & 15&\color{red}{.}& 2\color{green}{00} \\ - & \color{green}{0}3& \color{red}{.}&432 \\ \hline & 11& \color{red}{.}&768 \\ \end{compactarray}$$$

So, 15.2+(-3.432)=11.768.

So, how do we add decimals?

  1. Line up decimals (dot under the dot)
  2. Pad with zeros (if necessary)
  3. Add just like integers.

Also, if number has no decimal part (it is integer), just pad decimal part with required number of zeros. So, for example, 27 becomes 27.0 or 27.00 etc.

As you already guess, with this method (as with integers) we can add as many decimals, as we want.

Now, it's time to practice.

Exercise 1. Find `2.5+1.7`.

Answer: 4.2.

Exercise 2. Find `14.37+7`.

Answer: 21.37

Exercise 3. Find `-10.1+9.3`.

Answer: -0.8.

Exercise 4. Find `34.5+12.17+0.5`.

Answer: 47.17.

Exercise 5. Find `-1.3+120.8+3.5+(-4.2)+11.777`.

Answer: 130.577.