Data Source and Methodology
Authoritative Data Source: OpenStax, “Prealgebra 2e,” 2021. Direct link.
Tutti i calcoli si basano rigorosamente sulle formule e sui dati forniti da questa fonte.
Operations follow standard arithmetic laws (commutativity, associativity, distributivity) and order of operations (PEMDAS), implemented via a stable parsing algorithm (Shunting Yard) to transform expressions into Reverse Polish Notation for evaluation.
The Formula Explained
Core binary operations:
Addition: \( a + b \) Subtraction: \( a - b \)
Multiplication: \( a \times b \) Division: \( \dfrac{a}{b} \)
Exponent: \( a^{\,b} \)
Percent (postfix): \( a\% = \dfrac{a}{100} \)
Order of operations (highest to lowest): \( \% \rightarrow \text{unary } - \rightarrow \, ^ \rightarrow \times, \div \rightarrow +, - \)
Distributive property for reference: \( a(b+c) = ab + ac \)
Glossary of Variables and Fields
| Field | Definition |
|---|---|
| Expression | User input string containing numbers, operators, and parentheses. |
| + | Adds two values. |
| − | Subtracts right value from left value. |
| × | Multiplies two values. |
| ÷ | Divides left value by right value (right must not be zero). |
| % | Postfix percent operator; divides the preceding value by 100. |
| ^ | Exponentiation; raises left operand to the power of right operand. |
| Precision | Number of decimals used to display the result (0–12). |
| Format | Display style: standard or scientific notation. |
| Result | Final numeric value after evaluation. |
How It Works: A Step‑by‑Step Example
Scenario: Compute (12 + 3.5) × 2 − 50%
- Enter:
(12 + 3.5) × 2 − 50% - Normalize operators and apply percent: \( (12 + 3.5) \times 2 - \dfrac{50}{100} \)
- Evaluate parentheses: \( 12 + 3.5 = 15.5 \)
- Multiply: \( 15.5 \times 2 = 31 \)
- Percent term: \( 50\% = 0.5 \)
- Subtract: \( 31 - 0.5 = 30.5 \)
With precision 2, the displayed result is \( 30.50 \).
Frequently Asked Questions (FAQ)
What operations are supported?
Addition (+), subtraction (−), multiplication (×), division (÷), postfix percent (%), exponent (^), unary negative, and parentheses.
How do I type operators on the keyboard?
Use + - * / ^ ( ) and Enter to evaluate. The calculator converts * to × and / to ÷ visually.
How are errors handled?
You'll see clear inline messages for invalid characters, mismatched parentheses, incomplete expressions, or division by zero. Fix the highlighted issue and try again.
How does percent work in multi-step expressions?
Percent is applied to the value immediately before it. For example, 200 × 15% becomes 200 × 0.15.
Can I reuse results?
Yes, the History list stores recent calculations. Click Use to push a previous result back to the Expression field.
Is the calculator accessible?
Yes. It meets WCAG 2.1 AA guidelines: keyboard navigable, visible focus styles, screen reader announcements, and adequate color contrast.