Add decimals

Addition of finite decimals through the thousandths place is understood through place value: digits with the same value are aligned, equivalent trailing zeros may be inserted, and regrouping occurs across decimal places just as in whole-number addition. This connects decimal addition to fractions with denominators of 10, 100, or 1,000, measurement, and estimation; it excludes repeating decimals and more advanced generalizations beyond these place values.

Detailed Explanation: Add decimals

To add decimals, line up digits with the same place value. The decimal points should be directly above each other.

Example:

5.68+2.459

First, write the numbers with their decimal points aligned. Add a zero to make the first number have thousandths:

  5.680
+ 2.459

Now add from right to left:

Thousandths: $0+9=9$
Hundredths: $8+5=13$ . Write $3$ and regroup $1$ to the tenths place.
Tenths: $6+4+1=11$ . Write $1$ and regroup $1$ to the ones place.
Ones: $5+2+1=8$ .

The decimal point stays aligned:

  5.680
+ 2.459
-------
  8.139

Therefore,

5.68+2.459=\boxed{8.139}

The added zero does not change the value of $5.68$ because $5.68=5.680$ . You can estimate to check: $5.68$ is about $5.7$ , and $2.459$ is about $2.5$ , so the sum should be about $8.2$ . The answer $8.139$ is reasonable.

Learn by doing: Add decimals

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Addition - Decimal Thousandths (Column)

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Add decimals

Detailed Explanation: Add decimals

Learn by doing: Add decimals

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Addition - Decimal Thousandths (Column)