Perform basic arithmetic operations on decimal numbers.
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Result: 0.00
Understanding Decimal Arithmetic
Decimal numbers, also known as base-10 numbers, are fundamental to everyday mathematics and finance. They represent parts of a whole number using a positional notation system where each digit's value depends on its position relative to the decimal point. This calculator is designed to perform the four basic arithmetic operations—addition, subtraction, multiplication, and division—on two decimal numbers.
The Math Behind the Operations:
Addition: To add decimals, align the numbers vertically by their decimal points. Fill any empty places with zeros. Add the numbers column by column, carrying over as needed, and place the decimal point in the sum directly below the decimal points in the numbers being added.
Example: 12.34 + 5.678 Aligning:
12.340 + 5.678 ------- 18.018
Subtraction: Similar to addition, align the decimals and fill with zeros. Subtract column by column, borrowing as needed. Place the decimal point in the difference directly below the decimal points.
Example: 25.7 - 10.25 Aligning:
25.70 - 10.25 ------- 15.45
Multiplication: To multiply decimals, ignore the decimal points initially and multiply the numbers as if they were whole numbers. Then, count the total number of decimal places in the original numbers and place the decimal point in the product so that it has that total number of decimal places.
Example: 3.5 * 1.2 Multiply 35 * 12 = 420.
Total decimal places: 1 (in 3.5) + 1 (in 1.2) = 2.
Place decimal 2 places from the right: 4.20 or 4.2.
Division: To divide decimals, 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 the division as with whole numbers, placing the decimal point in the quotient directly above the decimal point in the dividend.
Example: 15.6 / 0.3 Move decimal 1 place right in 0.3 to get 3.
Move decimal 1 place right in 15.6 to get 156.
Divide 156 by 3 = 52.
Example: 8.4 / 2 Divisor is already whole.
Divide 8.4 by 2 = 4.2.
Use Cases:
Decimal calculations are ubiquitous. This calculator can be helpful for: