Convert between scientific notation, standard form, and expanded form with our free calculator. Get instant results for number format conversions and mathematical notation.
Convert between scientific notation, standard form, and expanded form
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Standard notation, scientific notation, and expanded form are different ways to represent numbers, each with specific advantages for different mathematical and scientific applications. Our Standard Notation Calculator makes it easy to convert between these formats with instant results.
Understanding these number representations is essential for working with very large or very small numbers, scientific calculations, and mathematical problem-solving. Each format serves different purposes and is used in various fields from physics and chemistry to engineering and finance.
Our calculator supports three types of conversions:
Simply select your conversion type, enter the number in the appropriate format, and click convert to get instant results with step-by-step explanations.
2,500,000
Regular decimal representation of numbers
Examples: 123, 45.67, 0.000123, 1,000,000
2.5 × 10^6
Numbers expressed as a × 10^n where 1 ≤ |a| < 10
Examples: 2.5 × 10^3, 1.23 × 10^-4, 6.02 × 10^23
2×10⁶ + 5×10⁵ + 0×10⁴ + 0×10³ + 0×10² + 0×10¹ + 0×10⁰
Numbers expressed as sum of powers of 10
Examples: 1234 = 1×10³ + 2×10² + 3×10¹ + 4×10⁰
Different number notations are used in various fields:
Standard notation is the regular decimal form (e.g., 2,500), while scientific notation expresses numbers as a × 10^n where 1 ≤ |a| < 10 (e.g., 2.5 × 10^3). Scientific notation is more compact for very large or small numbers.
Multiply the base by 10 raised to the exponent. For example, 2.5 × 10^3 = 2.5 × 1000 = 2,500. For negative exponents, divide by the appropriate power of 10.
Expanded form breaks down numbers into the sum of powers of 10. For example, 1234 = 1×10³ + 2×10² + 3×10¹ + 4×10⁰. It's used to understand place value and for educational purposes.
Yes, scientific notation can be written as '2.5 × 10^3' or '2.5e3'. Both formats are equivalent and widely accepted in scientific and engineering contexts.
Scientific notation is essential for expressing very large numbers (like distances in space) and very small numbers (like atomic sizes) in a compact, manageable format. It also makes calculations easier and shows significant digits clearly.
Understanding different number notations is fundamental to mathematics and science. Our Standard Notation Calculator simplifies conversions between scientific notation, standard form, and expanded form, making it easy to work with numbers in any format.
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