Decimal Calculator
Perform arithmetic operations with decimal numbers
Decimal Operations
Any decimal number
Any decimal number
Result
Examples
Addition Example
Problem: 12.3 + 1.719
Step 1: Align decimal points: 12.300 + 1.719
Step 2: Add as normal: 12.300 + 1.719 = 14.019
Answer: 14.019
Multiplication Example
Problem: 1.43 × 3.5
Step 1: Multiply as whole numbers: 143 × 35 = 5005
Step 2: Count decimal places: 2 + 1 = 3
Step 3: Place decimal 3 places from right: 5.005
Answer: 5.005
Division Example
Problem: 6.45 ÷ 1.5
Step 1: Multiply both by 100: 645 ÷ 150
Step 2: Divide: 645 ÷ 150 = 4.3
Answer: 4.3
Decimal Operation Rules
Addition/Subtraction
Align decimal points, then calculate
Multiplication
Count total decimal places in both numbers
Division
Convert to whole numbers first
Exponents
Use fraction form for decimal exponents
Common Fraction-Decimal Conversions
Calculation Tips
Always align decimal points for addition and subtraction
For multiplication, the result has as many decimal places as both numbers combined
Division can result in repeating decimals
Convert decimal exponents to fractions for exact calculations
Understanding Decimal Operations
What are Decimals?
Decimals are a way to represent fractions with denominators that are powers of 10. The decimal point separates the whole number part from the fractional part.
Place Value
Each digit after the decimal point represents a fraction: tenths (0.1), hundredths (0.01), thousandths (0.001), and so on.
Converting Fractions
To convert a fraction to a decimal, divide the numerator by the denominator. Some fractions result in terminating decimals, others in repeating decimals.
Precision and Rounding
When working with decimals, be aware of precision limits. Some operations may result in very long decimal expansions that need to be rounded.
Applications
- •Money calculations and financial operations
- •Scientific measurements and data analysis
- •Engineering calculations and precision work
- •Statistics and probability calculations