Precision Decimal Calculator
Perform addition, subtraction, multiplication, and division with decimal accuracy.
How to Calculate Decimals Manually
Calculating decimals is a fundamental mathematical skill used in engineering, science, and daily finance. While our decimal calculator provides instant results, understanding the underlying logic is essential for checking your work.
Addition and Subtraction
The most important rule for adding or subtracting decimals is to align the decimal points. If the numbers have a different number of digits after the decimal, you can add placeholder zeros to keep the columns straight.
Multiplication
When multiplying decimals, ignore the decimal points initially and multiply the numbers as if they were whole integers. Once you have the product, count the total number of digits to the right of the decimal points in both original numbers. Place the decimal point in your answer so that it has that same number of decimal places.
Division
To divide by a decimal, move the decimal point in the divisor (the number you are dividing by) to the right until it becomes a whole number. Move the decimal point in the dividend (the number being divided) the same number of places to the right. Then perform long division as usual.
Practical Calculation Examples
| Expression | Process | Result |
|---|---|---|
| 10.5 + 4.75 | Align points: 10.50 + 4.75 | 15.25 |
| 5.0 – 1.25 | Align points: 5.00 – 1.25 | 3.75 |
| 2.5 × 1.5 | 25 × 15 = 375 (move decimal 2 places) | 3.75 |
| 10.0 ÷ 2.5 | Move decimal: 100 ÷ 25 | 4.0 |
Frequently Asked Questions
What is a decimal? A decimal is a number expressed in the scale of tens. Often, "decimal" refers specifically to numbers that contain a fractional part separated from the whole number by a decimal point.
Why do calculators sometimes show 0.30000000000000004? This is known as floating-point inaccuracy. Computers use binary to represent decimals, which cannot perfectly represent some fractions like 0.1 or 0.2. Our calculator applies precision logic to minimize these errors.