Decimals Worksheets
Column addition and subtraction, and × ÷ by 10, 100, 1000 · Grades 4–6
Decimal practice on a notebook grid in two modes. Column mode adds and subtracts decimals with the decimal point on the grid line between the ones and the tenths, as in a squared exercise book, so a child lines up 3.8 under 12.75 by the point rather than by the last digit; choose one place, two places or a mix. Powers mode multiplies and divides by 10, 100 and 1000, where the point moves: the answer has a box for every digit and the child places the point. The decimal mark prints as a point or a comma, following the convention of each language.
Sheets are randomized, free to print, and carry no answer key on purpose – why Super Awesome Math works this way.
How to do it
Decimals follow the same column rules as whole numbers, with one addition: the decimal point marks the boundary between ones and tenths, and it must stay in its column.
- To add or subtract, write the numbers so the decimal points line up vertically, one under the other, and put the point in the answer directly below them.
- Fill any short number with zeros so both have the same number of decimal places. 3.5 + 0.75 becomes 3.50 + 0.75.
- Add or subtract column by column from the right exactly as with whole numbers, carrying and borrowing in the usual way.
- To multiply by 10, 100 or 1000, move the decimal point one, two or three places to the right. The digits do not change; only their columns do.
- To divide by 10, 100 or 1000, move it the same number of places to the left, adding zeros in front if you run out of digits.
Where it goes wrong
- Lining up the right-hand edges instead of the points. That puts the 5 of 3.5 under the 5 of 0.75, as though it were five hundredths, and 3.5 + 0.75 comes out as 0.80 instead of 4.25.
- Saying the digits move. It is easier to keep the digits still and move the point, but either way the point and the digits must not both move.
Frequently asked questions
- Why line up the decimal points instead of the last digits?
- In column addition of whole numbers the last digits line up because they are all ones. With decimals the last digit can be tenths in one number and hundredths in the other, so the point is what marks the ones column. 12.75 + 3.8 goes wrong the moment the 8 sits under the 5, and a point printed on the same grid line in every row makes that hard to do.
- Why does an answer like 16.0 keep its zero?
- The answer is written to as many places as the numbers above it, so the column stays full and a child checks every square. 12.5 + 3.5 is written 16.0 on the sheet and in the answer key; 16 is the same value, and either should be marked right.
- What happens to the decimal point when you multiply by 10?
- Every digit moves one place to the left, so the point appears to move one place right: 3.45 × 10 = 34.5, and × 100 gives 345. Dividing moves the digits the other way, which is why 27 ÷ 1000 needs zeros in front: 0.027. The answer has a box for every digit and none for the point, so where the point lands is the child’s to write.
- Why can I switch between a point and a comma?
- English-speaking and Chinese schools write 3.5, while French, Spanish, German, Italian and Russian schools write 3,5. The sheet starts with the convention of your language and remembers your choice, and several countries and international schools use the other mark, so it can be switched either way.
Settings
- Mode: column addition and subtraction, or × and ÷ by 10, 100 and 1000
- Operation: addition, subtraction or both
- Decimal places: one, two or a mix
- Decimal mark: a point or a comma
- Columns: 2, 3 or 4 (12–24 problems; 26 in powers mode)
- Print an answer key
Example problems
- 12.75 + 3.8 = □
- 20.4 − 7.35 = □
- 3.45 × 100 = □
- 27 ÷ 1000 = □
More Fractions & decimals
- Fractions – Simplify, find equivalent fractions and compare
- Add & Subtract Fractions – Like and unlike denominators, and mixed numbers