1. What is Decimal Expanded Form?

Decimal expanded form breaks down a number to show the value of each digit based on its position. For decimals, this includes both the integer part (whole numbers) and fractional part (after the decimal point).

2. How Does the Calculator Work?

The calculator uses the expanded form formula:

Where:

• Each digit is multiplied by 10 raised to the power of its position
• Positions to the left of the decimal point are positive (units, tens, hundreds)
• Positions to the right of the decimal point are negative (tenths, hundredths)

Example: 45.67 = 4×10¹ + 5×10⁰ + 6×10⁻¹ + 7×10⁻²

3. Importance of Expanded Form

Details: Understanding expanded form helps in learning place value, performing arithmetic operations, and converting between different number representations.

4. Using the Calculator

Tips: Enter any valid decimal number (positive or negative). The calculator will show 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 writes the number normally (e.g., 123.45), while expanded form shows each digit's value (1×100 + 2×10 + 3×1 + 4×0.1 + 5×0.01).

Q2: How does expanded form help with decimals?
A: It makes clear that digits after the decimal represent fractions (tenths, hundredths, etc.), helping understand decimal place value.

Q3: Can I enter negative decimals?
A: Yes, the calculator handles negative numbers by applying the negative sign to the entire expanded form.

Q4: What about repeating decimals?
A: The calculator shows the expanded form of the exact decimal entered. For repeating decimals, it will show the pattern in the expansion.

Q5: Why use powers of 10?
A: Our number system is base-10, so each position represents a power of 10, making this the natural way to expand numbers.