Adding Decimals to the Thousandths
Adding Decimals to the Thousandths (duplicate entry) is a Grade 5 math skill from Illustrative Mathematics Chapter 5 (Place Value Patterns and Decimal Operations) where students align decimal points vertically, add column by column starting from the right with regrouping as needed, and place the decimal point directly below in the sum. Trailing zeros can be used as placeholders to make numbers the same length for easier addition.
Key Concepts
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 $2.458 + 1.321 = 3.779$ $$ \begin{array}{r} &2&.&4&5&8 &\\ +&1&.&3&2&1 \\ \hline &3&.&7&7&9 \end{array} $$ $0.785 + 0.462 = 1.247$ $$ \begin{array}{r} &\overset{1}{0}&.&\overset{1}{7}&8&5 \\ +&0&.&4&6&2 \\ \hline &1&.&2&4&7 \end{array} $$ $4.5 + 3.298 = 7.798$ $$ \begin{array}{r} &4&.&5&0&0 \\ +&3&.&2&9&8 \\ \hline &7&.&7&9&8 \end{array} $$.
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.
Common Questions
How do you add decimals to the thousandths place?
Align the decimal points vertically and add from right to left, regrouping when a column's sum reaches 10 or more. Place the decimal point in the sum directly below the aligned decimal points in the addends.
What are trailing zeros in decimal addition?
Trailing zeros are zeros added at the end of a decimal to make it match the length of another decimal without changing its value. For example, 4.5 can be written as 4.500 to align with 3.298 for easier column addition.
Why is decimal addition the same as whole number addition?
The process is identical: add column by column from right to left with regrouping. The only additional step is aligning decimal points first and placing the decimal point in the sum in the same column.
What is an example of adding decimals to the thousandths?
2.458 + 1.321: add from right (8+1=9, 5+2=7, 4+3=7, 2+1=3) to get 3.779. For 0.785 + 0.462: 5+2=7, 8+6=14 (write 4 carry 1), 7+4+1=12 (write 2 carry 1), 0+0+1=1 gives 1.247.
What chapter in Illustrative Mathematics Grade 5 covers decimal addition?
Adding decimals to the thousandths is covered in Chapter 5 of Illustrative Mathematics Grade 5, titled Place Value Patterns and Decimal Operations.