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Add decimals

Decimal addition combines quantities within the base-ten place-value system: equivalent decimals may be expressed with trailing zeros, digits are aligned by place value rather than by the number of digits, and regrouping may occur across tenths, hundredths, thousandths, and whole-number places. Estimation and comparison of the sum with the addends help verify reasonableness, while the connection to fractions and measurement gives decimal notation meaning; the scope is finite decimals, not repeating decimals or more advanced algebraic generalizations.

Detailed Explanation: Add decimals

To add decimals, line up the decimal points. This places digits with the same value in the same column. You may add trailing zeros to make the columns easier to see.

Example: Find

12.58+3.74612.58+3.746

Rewrite 12.5812.58 as 12.58012.580:

  12.580
+  3.746
---------

Now add from right to left:

  1. Thousandths: 0+6=60+6=6. Write 66.
  2. Hundredths: 8+4=128+4=12. Write 22 and regroup 11 ten-hundredth into the tenths column.
  3. Tenths: 5+7+1=135+7+1=13. Write 33 and regroup 11 tenth into the ones column.
  4. Ones: 2+3+1=62+3+1=6.
  5. Tens: Bring down the 11.
  12.580
+  3.746
---------
  16.326

Therefore,

12.58+3.746=16.32612.58+3.746=\boxed{16.326}

To check that the answer is reasonable, estimate:

12.6+3.7≈16.312.6+3.7\approx16.3

The exact answer, 16.32616.326, is close to 16.316.3, so it makes sense.

Learn by doing: Add decimals

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    Addition - Decimal Hundredths

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