Decimal Addition Practice

Start by writing the numbers with their decimal points directly underneath one another. This puts units under units, tenths under tenths, and hundredths under hundredths. The number of digits in each number does not determine its position. For instance, when adding 12.68 and 4.7, the 4 belongs below the 2 because both represent units. The 7 belongs below the 6 because both represent tenths.

An empty place can be filled with a zero. Writing 4.7 as 4.70 leaves its value unchanged: seven tenths is seventy hundredths. Placeholder zeros are especially helpful when one number has several more decimal places than the other. They show exactly which columns have no additional quantity, so you do not have to keep track of empty spaces while calculating.

Add from the rightmost column towards the left. If a column totals ten or more, write its units digit and carry the remaining ten into the next column. Ten hundredths make one tenth, just as ten units make one ten. In 0.78 + 0.46, eight hundredths and six hundredths make fourteen hundredths. Write four in the hundredths column and carry one tenth into the tenths column.

Place the decimal point in the answer directly below the points in the numbers above. Addition does not require counting the total decimal places across both numbers. Your columns have already established where every place belongs. You can remove a trailing zero from a finished answer, but never remove a zero between the decimal point and a later nonzero digit.

Before checking your answer, make a rough estimate. A sum of 12.68 and 4.7 should be close to 13 + 5, so an answer near 18 is plausible. An answer near 1.8 or 180 would indicate a place value error. For a second check, subtract one addend from your total and confirm that the other remains.