Lesson 6: Decimal Addition: Sense Making and Estimation

Property

To add decimals, align the decimal points vertically. Add the digits in each place value column, starting from the right, and regroup as needed. Place the decimal point in the sum directly below the decimal points in the numbers being added.

Examples

• $2.458 + 1.321 = 3.779$

• $0.785 + 0.462 = 1.247$

• $4.5 + 3.298 = 7.798$

Explanation

This method for adding decimals is an application of place value. Aligning the decimal points ensures that you are adding digits with the same place value: thousandths to thousandths, hundredths to hundredths, and so on. If numbers have a different number of decimal places, you can add trailing zeros as placeholders. This process is similar to adding whole numbers, with the additional step of placing the decimal point in the final answer.

Property

To estimate the sum of decimals, round each decimal to a nearby whole number or another convenient place value (like the nearest tenth). Then, add the rounded numbers to find an approximate sum. This can be represented as: $a + b \approx \text{round}(a) + \text{round}(b)$.

Examples

• To estimate $4.9 + 7.2$, round $4.9$ to $5$ and $7.2$ to $7$. The estimated sum is $5 + 7 = 12$. The actual sum is $12.1$.
• To estimate $15.85 + 3.12$, round $15.85$ to $16$ and $3.12$ to $3$. The estimated sum is $16 + 3 = 19$. The actual sum is $18.97$.

Explanation

Estimating before you calculate helps you make sense of the numbers and predict a reasonable answer. By rounding decimals to the nearest whole numbers, you can perform a simpler addition problem in your head. This estimate serves as a valuable check to see if your final, precise answer is correct. If your calculated sum is very different from your estimate, you may have made a calculation error, like misaligning the decimal points.