Adding Decimals to the Thousandths
Adding Decimals to the Thousandths is a Grade 5 math skill from Illustrative Mathematics Chapter 5 (Place Value Patterns and Decimal Operations) where students learn to add decimals by aligning decimal points vertically, adding from right to left, regrouping as needed, and placing the decimal point directly below in the sum. Trailing zeros can be added as placeholders when decimal lengths differ, making this skill a direct extension of whole number 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 needed. Place the decimal point in the sum directly below the decimal points in the addends. Add trailing zeros to numbers with fewer decimal places to help with alignment.
What chapter covers adding decimals in Illustrative Mathematics Grade 5?
Adding decimals to the thousandths is covered in Chapter 5 of Illustrative Mathematics Grade 5, titled Place Value Patterns and Decimal Operations.
Why is aligning decimal points important when adding decimals?
Aligning decimal points ensures you are adding digits with the same place value — thousandths to thousandths, hundredths to hundredths, and so on. Misaligning decimal points leads to incorrect sums because you would be adding digits from different place values.
How do trailing zeros help when adding decimals?
When decimals have a different number of places after the decimal point, adding trailing zeros makes both numbers the same length. For example, 4.5 can be written as 4.500 to align with a number like 3.298, making column-by-column addition clearer.
What is an example of adding decimals to the thousandths?
To add 2.458 + 1.321, align decimal points and add column by column: 8+1=9, 5+2=7, 4+3=7, 2+1=3, giving 3.779. To add 0.785 + 0.462, regroup where needed: 5+2=7 (ones column), giving 1.247.