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Scientific Notation Calculator

Convert a number to scientific notation or back to standard form, with the E notation calculators use.

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Science and math are full of numbers too big or too small to write comfortably: 45,200,000 or 0.000000452. Scientific notation writes them as a short coefficient times a power of ten. This calculator converts either way and shows the E notation your calculator uses.

How to Use It

  1. Choose To Scientific Notation or To Standard Form.
  2. To convert to scientific notation, enter the Number. You can type E notation too, such as 6.02e23.
  3. To convert back, enter the Coefficient and the Power of 10.
  4. Press Calculate to see the number in both forms and in E notation.

How It Works

A number in scientific notation has a coefficient from 1 up to 10 and a whole-number power of ten:

number=a×10n1≤∣a∣<10\text{number} = \vA{a} \times 10^{\vB{n}} \qquad 1 \le |\vA{a}| < 10

To find n, count how many places the decimal point moves to leave one nonzero digit in front of it. Moving it left gives a positive n; moving it right gives a negative one.

Worked Example

For 45,200,000, the decimal point moves 7 places left to give 4.52:

45,200,000=4.52×10745{,}200{,}000 = 4.52 \times 10^{7}

For 0.000452, it moves 4 places right:

0.000452=4.52×10−40.000452 = 4.52 \times 10^{-4}

In E notation these are 4.52e7 and 4.52e-4.

Tips and Common Mistakes

  • Keep the coefficient between 1 and 10. 45.2 × 10⁶ has the right value but isn’t proper scientific notation; it’s 4.52 × 10⁷.
  • Small numbers get negative exponents. Anything between 0 and 1 has a power of ten below zero.
  • Multiply by adding exponents. 103×105=10810^3 \times 10^5 = 10^8; divide by subtracting them.
  • Watch significant figures. Trailing zeros after the decimal point are dropped here, so add them back when your answer needs them.
  • Read E carefully. On a calculator, 4.52E-4 means 4.52 × 10⁻⁴, not 4.52 minus 4.

Frequently Asked Questions

What is scientific notation?

A way of writing a number as a coefficient from 1 up to 10 times a power of 10. 45,200,000 is 4.52 × 10⁷ and 0.000452 is 4.52 × 10⁻⁴.

How do I know if the exponent is positive or negative?

Big numbers (10 or more) get a positive exponent, because the decimal point moves left. Numbers between 0 and 1 get a negative exponent, because it moves right.

What is E notation?

How calculators and spreadsheets show scientific notation: 4.52E7 means 4.52 × 10⁷. You can type it straight into the Number box.

Does the coefficient have to be between 1 and 10?

In proper scientific notation, yes. If you enter something like 45.2 × 10⁶ when converting back, the calculator also rewrites it properly as 4.52 × 10⁷.

How do I multiply numbers in scientific notation?

Multiply the coefficients and add the exponents, then tidy up: (2 × 10³) × (4 × 10⁵) = 8 × 10⁸.

Does it keep significant figures?

It keeps the digits you type but drops trailing zeros after the decimal point, so 4.50 × 10³ shows as 4.5 × 10³. Add the zeros back if your answer needs a set number of significant figures.

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