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Scientific Notation Calculator
Perform addition, subtraction, multiplication, and division on numbers in scientific notation, or convert between scientific notation and standard decimal form.
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Scientific Notation Converter
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Step-by-step
Understanding Scientific Notation
Scientific notation is a method of writing numbers that are too big or too small to be conveniently written in decimal form. It is written in the form:
a × 10b
Where 1 ≤ |a| < 10 (the coefficient) and b is an integer (the exponent).
Rules of Operations
- Multiplication: Multiply the coefficients and add the exponents: (a × 10x) × (b × 10y) = (a × b) × 10x + y.
- Division: Divide the coefficients and subtract the exponents: (a × 10x) ÷ (b × 10y) = (a ÷ b) × 10x - y.
- Addition & Subtraction: Align the exponents to the larger exponent, add/subtract the coefficients, and rewrite the final expression back into normalized form.
FAQ
What is normalized scientific notation?
Normalized scientific notation requires that the absolute value of the coefficient a is greater than or equal to 1, and strictly less than 10. For example, 12.5 × 103 is not normalized; it should be written as 1.25 × 104.
How do you convert negative exponents to decimal format?
A negative exponent tells you to move the decimal point to the left. For example, 3.5 × 10-3 requires moving the decimal point three places to the left, which results in 0.0035.