Adding and Subtracting Decimals to Thousandths

Adding and subtracting decimals is just like adding and subtracting whole numbers, but with one very important rule: always line up the decimal points!

When working with decimals up to the thousandths place (three digits after the decimal point), you might find that your numbers have different lengths. Here is the step-by-step method to solve them easily.

The Golden Rules of Decimals

1. Line 'em up: Write the numbers vertically so that the decimal points are stacked exactly on top of each other.
2. Fill in the blanks: Add placeholder zeros (trailing zeros) to the end of the shorter number so both numbers have the exact same number of decimal places.
3. Solve: Add or subtract exactly like you would with regular whole numbers.
4. Bring it down: Drop the decimal point straight down into your final answer.

Example 1: Adding Decimals

Problem: $12.456 + 3.78 = ?$

First, line up the decimal points vertically. Notice that $12.456$ has three decimal places (thousandths), but $3.78$ only has two (hundredths). Add a zero to $3.78$ to make it $3.780$.

$$\begin{array}{r} 12.456 \\ + \ 3.780 \\ \hline 16.236 \end{array}$$

Answer: $16.236$

Example 2: Subtracting Decimals

Problem: $8.003 - 2.147 = ?$

Both numbers already have three decimal places, so we don't need to add any zeros. Line up the decimal points and subtract. You will need to borrow just like you do with whole numbers!

$$\begin{array}{r} 8.003 \\ - \ 2.147 \\ \hline 5.856 \end{array}$$

Answer: $5.856$

Example 3: Estimating Your Answer

Sometimes, you just need a quick guess to check if your exact answer makes sense. You can do this by rounding each decimal to the nearest whole number before adding or subtracting.

Problem: Estimate $4.567 + 3.892$

1. Round $4.567$ to the nearest whole number: The tenths digit is $5$, so round up to $5$.
2. Round $3.892$ to the nearest whole number: The tenths digit is $8$, so round up to $4$.
3. Add the rounded numbers: $5 + 4 = 9$.

Estimate: $9$

(If we calculate the exact answer, $4.567 + 3.892 = 8.459$, which is very close to our estimate of $9$!)