How to use the scientific notation calculator
- Choose Convert a number or Calculate with two numbers.
- To convert, type the number as a decimal (0.00045), in E notation (6.02e23) or as a × 10n (3.1 × 104). Optionally set the number of significant figures to round to.
- To calculate, enter each number as a coefficient and a power of 10, then pick add, subtract, multiply or divide.
- Read the answer in scientific, E and engineering notation, plus the ordinary decimal form when it is short enough to write out.
How scientific notation works
The coefficient a holds the significant digits, with exactly one nonzero digit before the decimal point. The exponent n counts how many places the decimal point moved: positive for numbers of 10 or more, negative for numbers below 1. To multiply, multiply the coefficients and add the exponents. To divide, divide the coefficients and subtract the exponents. To add or subtract, first rewrite both numbers with the same power of ten. Then normalize: if the new coefficient is 10 or more, or below 1, shift its decimal point and adjust the exponent to match.
Worked example
The calculator opens with the speed of light, 299,792,458 m/s:
- Move the decimal point 8 places to the left, so that one nonzero digit sits in front of it: 299,792,458 → 2.99792458.
- Moving it 8 places left divides by 10⁸, so multiply by 10⁸ to keep the value: 2.99792458 × 10⁸.
- In E notation that is 2.99792458e+8. In engineering notation the exponent must be a multiple of 3, giving 299.792458 × 10⁶, or 299.792458 mega (M) meters per second.
For arithmetic, the default is (4.2 × 10⁵) × (3 × 10⁻²). Multiply the coefficients: 4.2 × 3 = 12.6. Add the exponents: 5 + (−2) = 3. That gives 12.6 × 10³, and normalizing moves one place: 1.26 × 10⁴. Dividing instead gives 4.2 ÷ 3 = 1.4 and 5 − (−2) = 7, so 1.4 × 10⁷.
Notations compared
| Number | Scientific | E notation | Engineering |
|---|---|---|---|
| 299,792,458 | 2.99792458 × 10⁸ | 2.99792458e+8 | 299.792458 × 10⁶ |
| 0.00045 | 4.5 × 10⁻⁴ | 4.5e-4 | 450 × 10⁻⁶ |
| 6,371,000 | 6.371 × 10⁶ | 6.371e+6 | 6.371 × 10⁶ |
| 0.0000000016 | 1.6 × 10⁻⁹ | 1.6e-9 | 1.6 × 10⁻⁹ |
Engineering notation lines up with metric prefixes: 10³ is kilo, 10⁶ mega, 10⁻³ milli, 10⁻⁶ micro and 10⁻⁹ nano. 450 × 10⁻⁶ meters is simply 450 micrometers.
Significant figures
Scientific notation removes the doubt about zeros. "1,200" could have two, three or four significant figures, but 1.2 × 10³ has two and 1.200 × 10³ has four. When you convert a whole number, the calculator treats its trailing zeros as placeholders. To keep them, type a decimal point (1200.) or set the number of significant figures. Leading zeros, as in 0.00045, are never significant.
Frequently asked questions
What does the E in 6.02E23 mean?
E stands for "times ten to the power". Calculators, spreadsheets and programming languages use it because a raised exponent is hard to type. 6.02E23 is 6.02 × 10²³, and 4.5E-4 is 4.5 × 10⁻⁴, or 0.00045.
How do I convert scientific notation back to a normal number?
Move the decimal point by the exponent: to the right for a positive exponent and to the left for a negative one, filling gaps with zeros. 3.1 × 10⁴ becomes 31,000 and 4.5 × 10⁻⁴ becomes 0.00045. Type either form into the converter and it shows the standard form too.
Why must the coefficient be less than 10?
It keeps every number in one standard form, so you can compare sizes at a glance by looking at the exponent. 45 × 10³ is correct arithmetic, but it should be written 4.5 × 10⁴. The calculator always normalizes its answers this way.
Can I enter a negative number?
Yes. A minus sign in front of the number makes the coefficient negative: -0.0032 is -3.2 × 10⁻³. That is different from a negative exponent, which only means the number is smaller than 1 in size.
Related calculators
- Rounding Calculator — Round to decimal places, significant figures, the nearest 10, 100 or 1,000, or the nearest fraction, with six rounding rules.
- Exponent Calculator — Raise any number to any power, including negative and fractional exponents, or solve for the exponent or the base.
- Big Number Calculator — Exact arithmetic on whole numbers with hundreds or thousands of digits: add, multiply, divide, powers, factorials and GCD.
- Log Calculator — Logarithms in base 10, base e (ln), base 2 or any base, and solve log equations for x or for the base.
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