Subtracting Decimals to the Thousandths
Subtracting Decimals to the Thousandths is a Grade 5 math skill from Illustrative Mathematics Chapter 5 (Place Value Patterns and Decimal Operations) where students subtract decimals by aligning decimal points, subtracting from right to left with regrouping as needed, and placing the decimal point in the result below the decimal points in the problem. Adding trailing zeros to numbers with fewer decimal places simplifies alignment and regrouping.
Key Concepts
Property To subtract decimals, align the numbers by their decimal points. Subtract as you would with whole numbers, starting from the rightmost place value, and regroup (borrow) when necessary. Place the decimal point in the difference directly below the decimal points in the numbers being subtracted.
Examples $5.432 2.156$ $$ \begin{array}{rcccccc} & 5 & . & \overset{3}{\cancel{4}} & \overset{12}{\cancel{3}} & \overset{12}{\cancel{2}} \\ & 2 & . & 1 & 5 & 6 \\ \hline & 3 & . & 2 & 7 & 6 \\ \end{array} $$.
$12.5 3.481$ $$ \begin{array}{rccccccc} & \overset{0}{\cancel{1}} & \overset{12}{\cancel{2}} & . & \overset{4}{\cancel{5}} & \overset{9}{\cancel{0}} & \overset{10}{\cancel{0}} \\ & & 3 & . & 4 & 8 & 1 \\ \hline & & 9 & . & 0 & 1 & 9 \\ \end{array} $$.
Common Questions
How do you subtract decimals to the thousandths place?
Align the decimal points vertically and subtract from right to left, regrouping (borrowing) when needed. Place the decimal point in the answer directly below the decimal points in the problem. Add trailing zeros to numbers with fewer decimal places to help alignment.
What chapter covers decimal subtraction in Illustrative Mathematics Grade 5?
Subtracting decimals to the thousandths is covered in Chapter 5 of Illustrative Mathematics Grade 5, titled Place Value Patterns and Decimal Operations.
What is an example of subtracting decimals to the thousandths?
To subtract 5.432 - 2.156, align decimal points and subtract column by column with regrouping: the result is 3.276. For 12.5 - 3.481, add trailing zeros to get 12.500 - 3.481 = 9.019.
Why do you add trailing zeros when subtracting decimals?
Trailing zeros extend a decimal to match the length of the other number without changing its value. This ensures proper alignment and makes regrouping easier when borrowing across different decimal places.
How is subtracting decimals similar to subtracting whole numbers?
The process is the same: subtract column by column from right to left, regrouping as needed. The only additional step is aligning decimal points first and placing the decimal point in the same column in the answer.