Subtracting Decimals

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

Example 1. Calculate `5.1-1.5`.

Line up decimals and perform subtraction:

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

So, 5.1-1.5=3.6.

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

Example 2. Calculate `21.72-15.9`.

Line up decimals and pad number 15.9 with zero:

$$$ \begin{compactarray}\ & 21&\color{red}{.}&72 \\ - & 15& \color{red}{.}&9\color{green}{0} \\ \hline & 5&\color{red}{.}&82 \\ \end{compactarray}$$$

So, 21.72-15.9=5.82.

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

This example also involves subtracting negative number from positive.

Example 3. Calculate `22.3-(-7.721)`.

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

Also, don't forget that subtracting negative number from positive actually means adding positive numbers.

$$$\begin{compactarray} \ & 22&\color{red}{.}& 3\color{green}{00} \\ + & \color{green}{0}7& \color{red}{.}&7.721 \\ \hline & 30& \color{red}{.}&021 \\ \end{compactarray}$$$

So, 22.3-(-7.721)=30.021.

So, how do we subtract decimals?

  1. Line up decimals (dot under the dot)
  2. Pad with zeros (if necessary)
  3. Subtract 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, 15 becomes 15.0 or 15.00 etc.

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

Exercise 1. Find `3.5-1.7`.

Answer: 1.8.

Exercise 2. Find `24-11.95`.

Answer: 12.05.

Exercise 3. Find `-10.5-9.3`.

Answer: -19.8.

Exercise 4. Find `34.9-12.71-0.235`.

Answer: 21.955.

Exercise 5. Find `-12.3-12-(-45.5)-(-4.048)-53.1`.

Answer: -27.852.