Scientific Notation Calculator
Type any number, as 0.000000123, 1.23e-7 or 1.23 × 10^-7, to see it in scientific, E, engineering and standard form, with how far the decimal point moved. Maths with two numbers does + − × ÷, powers and roots in scientific notation with every step. Advanced adds significant figures, rounding methods and sig fig rules.
Any style works: 0.000000123, 1.23e-7, 1.23E-07, 1.23 × 10^-7, 1.23 x 10^-7 or 10^5.
Type it the same way: 3.2 × 10^-2, 3.2e-2 or 0.032.
Auto keeps every digit you typed and every digit of an exact answer (up to 30), and rounds answers that never end to 15.
The half methods only differ when the dropped part is exactly half.
How your answer is worked out
Your number: find the first digit, move the decimal point next to it, then count the moves as a power of ten.
- 1
Find the first digit
0.000000123first digit: 1
- 2
Move the point
7 places right→ 1.23
- 3
Count the power
right = negative× 10⁻⁷
- 4
Write it out
1.23 × 10⁻⁷= 1.23e-7eng: 123 n
Read more: the rules, the formula, worked examples and SI prefixes
Scientific notation writes any number as a number from 1 to just under 10, times a power of ten. It turns hard-to-read numbers like 602,200,000,000,000,000,000,000 or 0.000000123 into short ones like 6.022 × 10²³ and 1.23 × 10⁻⁷. The power of ten tells you how many places the decimal point moved, and the number in front holds the significant figures.
The formula
number = a × 10ⁿ, where a is from 1 to just under 10 (ignoring the sign) and n is a whole number
n = how many places the decimal point moves to sit after the first non-zero digit (moving left = positive, moving right = negative)
E notation: a × 10ⁿ is typed a e n, like 1.23e-7
engineering notation: a × 10ⁿ with n a multiple of 3, so a is from 1 to 999
(a × 10ᵐ) × (b × 10ⁿ) = (a × b) × 10^(m + n)
(a × 10ᵐ) ÷ (b × 10ⁿ) = (a ÷ b) × 10^(m − n)
a × 10ᵐ ± b × 10ⁿ: rewrite both with the bigger power, then add or subtract the numbers in front
(a × 10ᵐ)ᵏ = aᵏ × 10^(m × k)
ᵏ√(a × 10ᵐ) = ᵏ√a × 10^(m ÷ k), after making m a multiple of k
then tidy up: if the number in front is 10 or more, or less than 1, move its point and change the power to match
Worked example
Converting 0.000000123. The first digit that isn’t zero is the 1. Move the decimal point 7 places to the right so it sits just after the 1, which gives 1.23. Moving right means the power of ten is negative, so the power is −7: 0.000000123 = 1.23 × 10⁻⁷, or 1.23e-7 in E notation. It has 3 significant figures (1, 2 and 3). For engineering notation, lower the power to the next multiple of 3, −9, and move the point 2 more places right: 1.23 × 10⁻⁷ = 123 × 10⁻⁹, which is 123 nano (123 n), or 123 billionths.
Multiplying (4.5 × 10⁶) × (3.2 × 10⁻²). Multiply the numbers in front: 4.5 × 3.2 = 14.4. Add the powers: 6 + (−2) = 4. That gives 14.4 × 10⁴. 14.4 is not between 1 and 10, so move its point 1 place left and add 1 to the power: 1.44 × 10⁵ = 144,000. Check: 4,500,000 × 0.032 = 144,000.
Adding (1.6 × 10⁻¹⁹) + (2.4 × 10⁻²⁰). The bigger power is 10⁻¹⁹, so rewrite 2.4 × 10⁻²⁰ as 0.24 × 10⁻¹⁹. Then 1.6 + 0.24 = 1.84, so the answer is 1.84 × 10⁻¹⁹.
A square root, √(1.44 × 10¹¹). The power 11 does not divide by 2, so move the point 1 place right and take 1 from the power: 14.4 × 10¹⁰. Then √14.4 ≈ 3.79473 and √10¹⁰ = 10⁵, so the answer is about 3.79473 × 10⁵.
Which way does the point move?
- Big numbers (10 and over): the point moves left, so the power is positive. 45,600,000 → 4.56 × 10⁷ (7 places left).
- Small numbers (under 1): the point moves right, so the power is negative. 0.00508 → 5.08 × 10⁻³ (3 places right).
- Numbers from 1 to 9.99…: the point stays put and the power is 0. 3.7 → 3.7 × 10⁰.
- Negative numbers keep their minus sign in front: −0.00508 = −5.08 × 10⁻³. A negative power never makes the number negative; it only makes it small.
SI prefixes for engineering notation
| Power | Prefix | Symbol |
|---|---|---|
| 10³⁰ | quetta | Q |
| 10²⁷ | ronna | R |
| 10²⁴ | yotta | Y |
| 10²¹ | zetta | Z |
| 10¹⁸ | exa | E |
| 10¹⁵ | peta | P |
| 10¹² | tera | T |
| 10⁹ | giga | G |
| 10⁶ | mega | M |
| 10³ | kilo | k |
| 10⁻³ | milli | m |
| 10⁻⁶ | micro | µ |
| 10⁻⁹ | nano | n |
| 10⁻¹² | pico | p |
| 10⁻¹⁵ | femto | f |
| 10⁻¹⁸ | atto | a |
| 10⁻²¹ | zepto | z |
| 10⁻²⁴ | yocto | y |
| 10⁻²⁷ | ronto | r |
| 10⁻³⁰ | quecto | q |
Ronna, quetta, ronto and quecto were added to the SI in November 2022 (27th General Conference on Weights and Measures). Number names use the short scale used in the US and UK today (a billion is 10⁹).
Significant figures
Every digit in the number in front counts as a significant figure, so scientific notation shows precision clearly. 45,600,000 is written 4.56 × 10⁷ because the zeros at the end are only placeholders. If they were measured, type 45600000. with a point and it becomes 4.5600000 × 10⁷. In Advanced you can round to any number of significant figures with 10 rounding methods, or round a sum by the sig fig rules: adding and subtracting keep the decimal places of the least precise number, multiplying and dividing keep the fewest significant figures.
All answers use exact decimal maths on the digits you typed, not binary floating point: 0.1 + 0.2 is exactly 0.3, and powers of ten from −1,000,000 to 1,000,000 can be typed (answers go up to 10¹⁵ as a power). Divisions, roots and decimal powers that never end are worked to 50 digits and shown to 15 significant figures (or the number you pick), marked with ≈.
Common questions
How do you write a number in scientific notation?
Move the decimal point so it sits just after the first digit that is not zero, which gives a number between 1 and 10. Then count how many places you moved it: that is the power of ten. Moving left gives a positive power and moving right gives a negative one. So 45,600,000 = 4.56 × 10⁷ and 0.000000123 = 1.23 × 10⁻⁷.
What is E notation, like 1.23e-7?
E notation is scientific notation typed on one line. The e (or E) means “times ten to the power”, so 1.23e-7 is 1.23 × 10⁻⁷ and 6.022E+23 is 6.022 × 10²³. Calculators, spreadsheets like Excel and programming languages use it because they cannot show a raised power.
What is the difference between scientific and engineering notation?
Scientific notation keeps one digit before the decimal point (1.23 × 10⁻⁷). Engineering notation only uses powers of ten that are multiples of 3, so the number in front is from 1 to 999 (123 × 10⁻⁹). That matches the SI prefixes, so 123 × 10⁻⁹ metres is 123 nanometres (123 nm).
How do you multiply numbers in scientific notation?
Multiply the numbers in front and add the powers. (4.5 × 10⁶) × (3.2 × 10⁻²) = 14.4 × 10⁴. Then tidy up so the front is between 1 and 10: 14.4 × 10⁴ = 1.44 × 10⁵. To divide, divide the numbers in front and subtract the powers.
How do you add numbers in scientific notation?
First give both numbers the same power of ten. For 1.6 × 10⁻¹⁹ + 2.4 × 10⁻²⁰, rewrite the second as 0.24 × 10⁻¹⁹. Then add the numbers in front: 1.6 + 0.24 = 1.84, so the answer is 1.84 × 10⁻¹⁹.
Why does my calculator show 0.30000000000000004?
Most calculators and computers store numbers in binary, and 0.1 and 0.2 cannot be stored exactly, so tiny errors show up. They also stop at about 1.8 × 10³⁰⁸ and 4.9 × 10⁻³²⁴. This calculator works with the decimal digits you typed, so 0.1 + 0.2 is exactly 0.3, and numbers like 1 × 10³⁰⁹ or 1 × 10⁻³⁵⁰ are no problem.
Is 0 in scientific notation 0 × 10⁰?
Yes. Zero has no first non-zero digit, so the number in front is 0 and any power of ten gives the same answer. The usual way to write it is 0 × 10⁰, or 0e+0 in E notation.
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