Scientific Notation Calculator
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0.000345 = 3.45 × 10⁻⁴
Scientific notation: 3.45 × 10⁻⁴ E-notation: 3.45E-4 Engineering notation: 345 × 10⁻⁶ (μ, micro) Decimal: 0.000345
How to use the scientific notation calculator
- Choose Convert a number or Calculate with two numbers.
- Type numbers in any form: 0.000345, 3.45e-4, 3.45E-4 or 3.45 × 10^-4 (you can type x or * for ×).
- Optionally set the number of significant figures to round to. Leave it blank to keep every digit.
- Copy the result in the form you need. E-notation is what most calculators, spreadsheets and programming languages accept.
Scientific notation rules
(a × 10ᵐ) × (b × 10ⁿ) = (a × b) × 10ᵐ⁺ⁿ
(a × 10ᵐ) ÷ (b × 10ⁿ) = (a ÷ b) × 10ᵐ⁻ⁿ
Add or subtract: rewrite with the same power of 10 first
Engineering notation: the power is a multiple of 3 (k, M, G, m, μ, n …)
The number in front (the coefficient or mantissa) carries the significant digits, and the exponent n counts how many places the decimal point moved: to the left for large numbers (positive n) and to the right for small ones (negative n). After multiplying or dividing, the coefficient may fall outside 1 to 10, so it is normalized by moving the point once more and adjusting the exponent. E-notation writes the same thing on one line, so 3.45E-4 means 3.45 × 10⁻⁴.
Worked example: how long sunlight takes to reach Earth
The speed of light is exactly 299,792,458 m/s, or 2.99792458 × 10⁸, and the astronomical unit (the mean Earth–Sun distance) is exactly 149,597,870,700 m, or 1.495978707 × 10¹¹. Dividing distance by speed:
- Divide the numbers and subtract the powers: (1.495978707 × 10¹¹) ÷ (2.99792458 × 10⁸) = (1.495978707 ÷ 2.99792458) × 10^(11 − 8)
- = 0.49900478383615641191 × 10³
- In scientific notation (1 ≤ number < 10): 4.9900478383615641191 × 10²
Rounded to four significant figures that is 4.990 × 10² seconds, or about 8.3 minutes.
Multiplying and adding
Multiply the numbers and add the powers: (3.2 × 10⁵) × (4.5 × 10⁴) = (3.2 × 4.5) × 10^(5 + 4) = 14.4 × 10⁹ In scientific notation (1 ≤ number < 10): 1.44 × 10¹⁰ For addition the powers must match first: Write both with the larger power, 10⁵: 4.5 × 10⁴ = 0.45 × 10⁵; Add the numbers in front: (3.2 + 0.45) × 10⁵ = 3.65 × 10⁵.
One number in every notation
| Decimal | Scientific | E-notation | Engineering | SI prefix |
|---|---|---|---|---|
| 602,214,076,000,000,000,000,000 | 6.02214076 × 10²³ | 6.02214076E23 | 602.214076 × 10²¹ | Z (zetta) |
| 47,000 | 4.7 × 10⁴ | 4.7E4 | 47 × 10³ | k (kilo) |
| 1,234,000 | 1.234 × 10⁶ | 1.234E6 | 1.234 × 10⁶ | M (mega) |
| 0.0047 | 4.7 × 10⁻³ | 4.7E-3 | 4.7 × 10⁻³ | m (milli) |
| 0.000345 | 3.45 × 10⁻⁴ | 3.45E-4 | 345 × 10⁻⁶ | μ (micro) |
| 0.000000065 | 6.5 × 10⁻⁸ | 6.5E-8 | 65 × 10⁻⁹ | n (nano) |
The first row is the Avogadro constant, 6.02214076 × 10²³ per mole, which is exact by definition in the SI.
Tips and common mistakes
- Check the coefficient. 45 × 10³ is a correct value but not scientific notation; normalize it to 4.5 × 10⁴.
- Negative exponents are small, not negative numbers. 3 × 10⁻⁴ = 0.0003 is positive; −3 × 10⁴ is a negative number.
- Significant figures live in the coefficient. 5.00 × 10⁻² has three, which is why the calculator keeps the zeros you type after a decimal point. In a whole number like 1200, trailing zeros are ambiguous, and scientific notation settles it: 1.2 × 10³ or 1.200 × 10³.
- E is not e. On calculators, 2E3 means 2 × 10³ = 2,000, not 2 × 2.718… × 3.
- To round a result, use the significant figures box or the rounding calculator. For exact answers with hundreds of digits, use the big number calculator.
Frequently asked questions
How do I write a number in scientific notation?
Move the decimal point until one non-zero digit is in front of it, then count the moves. For 0.000345 the point moves 4 places right, so it is 3.45 × 10⁻⁴; for 1,234,000 it moves 6 places left, giving 1.234 × 10⁶.
What is E-notation?
E-notation writes scientific notation on one line: the E means “times ten to the power of”. 3.45E-4 is 3.45 × 10⁻⁴ = 0.000345, and 6.02E23 is 6.02 × 10²³.
What is engineering notation?
It is like scientific notation but the exponent is always a multiple of 3, so it lines up with SI prefixes. 0.000345 is 345 × 10⁻⁶ (345 micro-units), and 47,000 is 47 × 10³ (47 k).
How do you multiply numbers in scientific notation?
Multiply the coefficients and add the exponents, then normalize. (3.2 × 10⁵) × (4.5 × 10⁴) = 14.4 × 10⁹ = 1.44 × 10¹⁰.
How do you add numbers in scientific notation?
Rewrite them with the same power of ten, add the coefficients, then normalize. 3.2 × 10⁵ + 4.5 × 10⁴ = 3.2 × 10⁵ + 0.45 × 10⁵ = 3.65 × 10⁵.