Scientific Notation Calculator
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Enter standard notation to convert to scientific notation
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Scientific Notation
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Scientific notation
E-notation
Standard form
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Scientific Notation Format & Rules
Scientific notation expresses any number as a × 10^n, where 1 ≤ |a| < 10 (the coefficient) and n is an integer (the exponent). It is the universal standard in science and engineering for expressing very large and very small numbers without writing dozens of zeros.
In E-notation (used in calculators and code): 2.998E8 = 2.998 × 10^8. This is identical in meaning but more compact for digital display.
Converting to Scientific Notation
299,792,458: move decimal 8 places left = 2.99792458. Exponent = 8. Result: 2.998 × 10^8. For 0.00042: move right 4 places. Result: 4.2 × 10^−4.
Multiplying in Scientific Notation
(3 × 10^8) × (2 × 10^3): multiply coefficients (3×2=6), add exponents (8+3=11). Result: 6 × 10^11. If coefficient ≥10, adjust.
Dividing in Scientific Notation
(6 × 10^8) ÷ (2 × 10^3): divide coefficients (6/2=3), subtract exponents (8−3=5). Result: 3 × 10^5.
Large Number Reference
Million = 10^6. Billion = 10^9. Trillion = 10^12. Light-year ≈ 9.461 × 10^15 m. Atoms in universe ≈ 10^80. Googol = 10^100.
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Scientific Notation Questions
What is scientific notation?+
Scientific notation expresses numbers as a × 10^n, where 1 ≤ |a| < 10. Example: 93,000,000 miles (Earth-Sun distance) = 9.3 × 10^7. 0.000000001 = 1 × 10^−9. It makes very large and very small numbers manageable and immediately communicates the order of magnitude. It is the standard in science, engineering, astronomy, and physics.
How do I convert a number to scientific notation?+
(1) Move the decimal point so exactly one non-zero digit is to its left. (2) Count the places moved — that is the exponent. Moving left gives a positive exponent; moving right gives a negative exponent. (3) Write in the form a × 10^n. Example: 0.0045. Move right 3 places: 4.5. Exponent: −3. Result: 4.5 × 10^−3.
How do I multiply numbers in scientific notation?+
Multiply the coefficients and add the exponents. (3 × 10^4) × (5 × 10^6) = (3 × 5) × 10^(4+6) = 15 × 10^10. If the resulting coefficient is ≥10 or <1, adjust: 15 × 10^10 = 1.5 × 10^11. This adjustment keeps the result in proper scientific notation form.
How do I divide numbers in scientific notation?+
Divide the coefficients and subtract the exponents. (8 × 10^9) ÷ (4 × 10^3) = (8/4) × 10^(9−3) = 2 × 10^6. If the coefficient falls outside 1≤|a|<10, adjust. Example: (3 × 10^5) ÷ (6 × 10^2) = 0.5 × 10^3 = 5 × 10^2. The subtraction of exponents makes division of very large numbers straightforward.
What is E-notation?+
E-notation (used in calculators, spreadsheets, and programming languages) replaces "× 10^" with "E". 2.998E8 = 2.998 × 10^8 = 299,800,000. 4.5E−3 = 4.5 × 10^−3 = 0.0045. E-notation is identical in meaning to standard scientific notation, just more compact for digital display. In Python, JavaScript, and most programming languages, E-notation is the standard way to write scientific numbers in code.
How do I add numbers in scientific notation?+
Convert both to the same exponent first, then add the coefficients. (3 × 10^5) + (4 × 10^4) = (3 × 10^5) + (0.4 × 10^5) = 3.4 × 10^5. This is why addition/subtraction in scientific notation is more involved than multiplication/division — you need a common exponent before combining. Alternatively, convert both to standard notation, add, then convert back.
What are common examples of scientific notation in science?+
Speed of light: 2.998 × 10^8 m/s. Distance from Earth to Sun: 1.496 × 10^11 m. Mass of an electron: 9.109 × 10^−31 kg. Avogadro's number: 6.022 × 10^23 mol^−1. Planck's constant: 6.626 × 10^−34 J·s. Charge of an electron: 1.602 × 10^−19 C. Scientific notation is the only practical way to write these quantities.
What is a googol and how does it relate to scientific notation?+
A googol is 10^100 — a 1 followed by 100 zeros. In scientific notation: 1 × 10^100. A googolplex is 10^(10^100). The estimated number of atoms in the observable universe is approximately 10^80 — far less than a googol. The company "Google" was named after "googol." Scientific notation lets us meaningfully compare these astronomical numbers and see their relative sizes at a glance.
What is the difference between significant figures and scientific notation?+
Significant figures indicate precision — how many digits are meaningful. Scientific notation makes significant figures explicit: 3.00 × 10^8 has 3 significant figures; 3 × 10^8 has 1. In standard notation, 300 is ambiguous (1, 2, or 3 sig figs?). Scientific notation resolves this ambiguity. Scientists use scientific notation partly to communicate precision unambiguously alongside magnitude.
How do I convert from scientific notation back to standard form?+
Move the decimal point in the coefficient the number of places indicated by the exponent. Positive exponent: move right (large number). Negative exponent: move left (small number). Examples: 3.45 × 10^4 = 34,500 (move decimal right 4 places). 2.1 × 10^−3 = 0.0021 (move decimal left 3 places). Fill in zeros as needed.