A free decimal calculator that adds, subtracts, multiplies and divides decimal numbers, then shows the full working. Answers are exact, so 0.1 + 0.2 gives 0.3 — not 0.30000000000000004.
A decimal calculator adds, subtracts, multiplies or divides numbers that contain a decimal point. For addition and subtraction, line up the decimal points before you calculate. For multiplication, multiply normally and then place the point using the total number of decimal places. For division, shift the point in the divisor until it is a whole number and shift the dividend's point by the same amount.
1.005 can round to 1.00 instead of 1.01. This tool turns every entry into whole-number arithmetic behind the scenes, so the working matches what you would get by hand.The tool is built for quick, accurate arithmetic in four steps:
.75, leading zeros like 0.75, trailing zeros like 4.500, and negative values like -3.5.A decimal number uses a decimal point to show values smaller than one. The digits to the left of the point are whole numbers; the digits to the right are fractions of one, written in the base-10 system. Each place to the right is ten times smaller than the place before it: tenths, then hundredths, then thousandths, and so on.
For example, in 4.725 the 7 means seven tenths (0.7), the 2 means two hundredths (0.02), and the 5 means five thousandths (0.005). A whole number such as 6 is simply a decimal with nothing after the point.
Every decimal operation follows one idea: remove the decimal point, do whole-number arithmetic, then put the point back in the right place. The rule for placing the point is what changes between operations.
Write the numbers so the decimal points sit directly above one another, fill any short columns with zeros, then add column by column from the right. The point in the answer stays in the same column.
12.45 + 3.7 as 12.45 + 3.70 keeps every place value in its own column and prevents the most common mistake.Subtraction works the same way: align the points, pad with zeros so both numbers have the same number of decimal places, then subtract column by column, borrowing where needed. 8.2 − 3.75 becomes 8.20 − 3.75 = 4.45.
Ignore the points and multiply as whole numbers. Then count the total number of decimal places in all the numbers, and give the answer that many places. 2.4 × 1.25: multiply 24 × 125 = 3000, then place three decimals → 3.000 = 3.
0.3 × 0.3 should be small, near 0.1, so 0.09 looks right while 0.9 or 9 would signal a misplaced point.Shift the decimal point in the divisor (the number you divide by) until it becomes a whole number, then shift the dividend's point by the same number of places. Now it is ordinary long division. 7.5 ÷ 0.5 becomes 75 ÷ 5 = 15.
1 ÷ 3 = 0.333… The calculator shows a repeating block in brackets, like 0.(3), and labels a cut-off answer as rounded.These are the core rules the calculator follows, and the ones worth memorising:
| Operation | Rule | Quick example |
|---|---|---|
| Addition | Align points, add columns | 2.5 + 1.25 = 3.75 |
| Subtraction | Align points, subtract columns | 5.2 − 1.75 = 3.45 |
| Multiplication | Multiply, count all places | 1.2 × 0.5 = 0.6 |
| Division | Make divisor whole, then divide | 4.8 ÷ 0.6 = 8 |
| × by 10ⁿ | Point moves right n places | 3.14 × 100 = 314 |
| ÷ by 10ⁿ | Point moves left n places | 3.14 ÷ 100 = 0.0314 |
4.75 + 2.6 → align to 4.75 + 2.60 → add columns → 7.35.
12.4 + 0.056 → align to 12.400 + 0.056 → 12.456. The zeros make the columns match.
10.00 − 3.275 → subtract with borrowing → 6.725.
2.5 × 1.2 → 25 × 12 = 300 → two decimal places → 3.00 → 3.
7.5 ÷ 0.25 → shift two places → 750 ÷ 25 → 30.
-3.5 + 1.25 → the negative number is larger, so the answer is negative → -2.25.
Using the number 345.678, each digit sits in a place ten times smaller than the one to its left:
| Place | Digit | Value |
|---|---|---|
| Hundreds | 3 | 300 |
| Tens | 4 | 40 |
| Ones | 5 | 5 |
| Tenths | 6 | 0.6 |
| Hundredths | 7 | 0.07 |
| Thousandths | 8 | 0.008 |
| Operation | Main rule | Example | Answer |
|---|---|---|---|
| Addition | Align decimal points | 2.5 + 1.25 | 3.75 |
| Subtraction | Align decimal points | 5.2 − 1.75 | 3.45 |
| Multiplication | Count decimal places | 1.2 × 0.5 | 0.6 |
| Division | Make divisor whole | 4.8 ÷ 0.6 | 8 |
A decimal place is a position to the right of the point. Rounding to two decimal places keeps two digits after the point; if the third digit is 5 or more, the second digit rounds up. This calculator offers optional rounding so you can match the precision you need — two places for money, more for science.
For detailed control such as significant figures, rounding modes, or rounding a single number on its own, use the dedicated Rounding Calculator.
0.5 as 5, or dropping a meaningful zero.0.30000000000000004 as exact.3,14 for 3.14. The base-10 idea behind it is the same everywhere.Decimal arithmetic shows up almost everywhere: money and shopping totals, measurements and distances, weights, fuel and travel, construction and DIY cutting lists, science and lab work, business figures, sports scores and averages, and everyday school maths. Any time a quantity falls between whole numbers, decimals do the work.
Try these by hand, then reveal the answers to check.
2.5 + 1.4 = 3.9 · 7.8 − 3.2 = 4.6 · 0.4 × 0.5 = 0.2 · 6.3 ÷ 0.9 = 7 · 1.25 + 2.75 = 4
12.045 + 0.98 = 13.025 · 20 − 3.675 = 16.325 · 4.25 × 0.16 = 0.68 · 9.6 ÷ 0.24 = 40 · −7.5 + 3.125 = −4.375
A decimal calculator adds, subtracts, multiplies or divides numbers that contain a decimal point, and shows the step-by-step working so you can follow the method rather than just copy the answer.
Do the whole-number arithmetic first, then place the decimal point using the rule for that operation: align points for adding and subtracting, count places for multiplying, and make the divisor whole for dividing.
Write the numbers with their decimal points lined up, fill short columns with zeros, then add each column from the right. The answer's point stays in the same column.
Line up the points, pad with zeros so both numbers have the same number of decimal places, then subtract column by column, borrowing where needed. For example, 8.20 − 3.75 = 4.45.
Multiply as whole numbers, then count the total decimal places in all the numbers and give the answer that many places. 2.4 × 1.25 → 24 × 125 = 3000 → three places → 3.000 = 3.
Shift the divisor's point to make it a whole number, shift the dividend's point by the same amount, then divide. 7.5 ÷ 0.5 becomes 75 ÷ 5 = 15.
Aligning the points keeps digits of the same place value in the same column — tenths under tenths, hundredths under hundredths — so you add or subtract matching values instead of mixing them up.
Yes. Put a minus sign in front of any number, such as -3.5. Negative values work across all four operations.
Yes. Dividing by a whole number is the simplest case — the divisor is already whole, so you just divide and keep the decimal point in line, as in 4.8 ÷ 6 = 0.8.
Yes. Move the divisor's point to make it whole, move the dividend's point the same number of places, then divide the resulting numbers.
Division by zero has no defined answer, so the calculator shows the message “Division by zero is not defined.” instead of a result.
Choose a number of decimal places from the rounding menu before calculating. The result shows both the exact value (where it exists) and the rounded value, along with how many places were used.
A terminating decimal ends after a set number of digits, such as 0.75 or 3.125. Its digits do not repeat forever.
A repeating (or recurring) decimal has one or more digits that repeat without end, such as 0.333… from 1 ÷ 3. This calculator marks the repeating block in brackets, like 0.(3).
Most software stores decimals in binary floating-point, which cannot hold 0.1 or 0.2 exactly, so tiny errors appear and you might see 0.30000000000000004. This tool uses whole-number arithmetic and returns exactly 0.3.
Methodology & purpose. All arithmetic runs on exact integer (BigInt) maths rather than binary floating-point, so results match hand calculations; non-terminating divisions are clearly labelled as rounded. This page is for general educational use and does not provide financial, tax or legal advice.