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
- Choose To Scientific Notation or To Standard Form.
- To convert to scientific notation, enter the Number. You can type E notation too, such as 6.02e23.
- To convert back, enter the Coefficient and the Power of 10.
- 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:
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:
For 0.000452, it moves 4 places right:
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. ; 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.