1. What is Expanded Form?

Expanded form is a way to write numbers by showing the value of each digit. It breaks down a number to show how much each digit in the number represents based on its place value.

2. How Does the Calculator Work?

The calculator uses the expanded form formula:

Where:

• \( \text{digit} \) — Each digit in the number
• \( \text{position} \) — The position of the digit (starting from 0 at the ones place)
• Positive exponents for integer part
• Negative exponents for decimal part

Example: 123.45 = 1×10² + 2×10¹ + 3×10⁰ + 4×10⁻¹ + 5×10⁻²

3. Importance of Expanded Form

Details: Expanded form helps understand place value and the composition of numbers. It's particularly useful in teaching mathematics and for understanding large numbers.

4. Using the Calculator

Tips: Enter any number (positive or negative, integer or decimal). The calculator will break it down into its expanded form showing each digit's value based on its position.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between standard and expanded form?
A: Standard form is the normal way we write numbers (e.g., 456). Expanded form shows the value of each digit (400 + 50 + 6).

Q2: How do you write zero in expanded form?
A: Digits that are zero are typically omitted in expanded form since they don't contribute to the value.

Q3: Can expanded form be used with decimals?
A: Yes, decimal places use negative exponents (e.g., 0.5 = 5 × 10⁻¹).

Q4: What's the expanded form of negative numbers?
A: The negative sign is placed before the expanded form (e.g., -123 = -(100 + 20 + 3)).

Q5: Is there a limit to the size of numbers this can handle?
A: The calculator can handle very large and very small numbers within PHP's floating-point precision limits.