What this calculator does
Turn a very big or very small number into short scientific notation, or turn it back into a full decimal. Scientific notation writes a number as a short number times a power of ten. The short number in front, called the coefficient, is between 1 and 10. The power of ten tells you how many places the decimal point moves.
For example, the speed of light, 299,792,458 m/s, becomes 2.998 × 10⁸ when you keep four significant figures (the digits that carry real information). The charge of an electron, 0.0000000000000000001602 coulombs, becomes 1.602 × 10⁻¹⁹. Written this way, huge and tiny numbers are easy to read, and you can see at a glance how precise they are.
The calculator works in both directions. Give it a decimal and how many significant figures to keep, and you get scientific, E and engineering notation. Or give it the number in front and a power of ten, and you get the full decimal with every zero written out.
Where it's used
Why this math matters outside the classroom:
- Astronomy. Astronomers write the Sun's distance from Earth, about 150,000,000 km, as 1.5 × 10⁸ km.
- Cell sizes. A red blood cell about 0.000008 m across is written as 8 × 10⁻⁶ m.
- Chemistry. Chemists work with Avogadro's number, 6.022 × 10²³ particles per mole, which takes 24 digits to write out in full.
- Calculator displays. A calculator showing 3.2E-7 means 3.2 × 10⁻⁷, or 0.00000032.
- Electronics. Engineers write a 4,700,000 ohm resistor in engineering notation as 4.7 × 10⁶ ohms, or 4.7 megohms.
Grade level and standards: Grade 8; Common Core State Standards for Mathematics 8.EE.A.4, 8.EE.A.3. © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.
How to use it
- Choose a direction: decimal to scientific, or scientific to decimal.
- For decimal to scientific, type the number. You can write it out or use E form, such as 6.02e23. Then choose how many significant figures to keep.
- For scientific to decimal, enter the number in front and the whole-number power of ten. A number in front outside 1–10, such as 45 × 10³, is fine; the calculator tidies it up for you.
- Read your answers and the steps. They show how far the decimal point moves and how the number in front is rounded.
What the inputs mean
- Number
- Type it out (0.000123) or in E form (1.23e-4).
- Significant figures
- How many digits to keep, counting from the first digit that isn't zero. Zeros at the end are kept when they count, so 1200 to three significant figures is 1.20 × 10³.
- Coefficient
- The number in front, usually between 1 and 10.
- Power of ten
- The small raised number on the 10, also called the exponent. A positive power makes the number bigger, because the decimal point moves right. A negative power makes it smaller, because the point moves left.
Formula and method
x = a × 10ⁿ, 1 ≤ |a| < 10, n = position of the first nonzero digit engineering: x = a × 10ᵐ, m a multiple of 3, 1 ≤ |a| < 1000 E notation: a × 10ⁿ is written aEn (for example 2.998e8)
In the formulas, x is your number, a is the number in front, and n (or m) is the power of ten. The bars in |a| mean "the size of a, ignoring any minus sign". To convert, move the decimal point until exactly one digit that isn't zero sits in front of it. The number of places you moved is the power.
The power is positive if you moved left, because the number was large. It's negative if you moved right, because the number was smaller than 1. Next, the number in front is rounded to the significant figures you chose. If rounding pushes it up to 10, the power goes up by one.
Engineering notation only uses powers that are multiples of 3. That lines it up with metric prefixes: 10³ is kilo and 10⁻⁶ is micro. So the number in front can have one to three digits before the point.
Worked example
Write the speed of light, 299,792,458 m/s, in scientific notation to 4 significant figures.
- Move the decimal point 8 places to the left: 299,792,458 = 2.99792458 × 10⁸.
- Round the number in front to 4 significant figures. The fifth digit is 9, so 2.997 rounds up to 2.998.
- Scientific notation: 2.998 × 10⁸, or 2.998e8 in E notation.
- For engineering notation, shift to a power that's a multiple of 3: 299.8 × 10⁶.
Result: 299,792,458 ≈ 2.998 × 10⁸ = 299.8 × 10⁶ m/s. That's 299.8 million meters per second.
Understanding the result
The power tells you how big a number is at a glance. Each step of 1 is a factor of 10. A number with a power of 8 is in the hundreds of millions. One with a power of −19 is smaller than a billionth of a billionth.
The number of digits in front shows how precise the number is. 2.998 × 10⁸ claims four significant figures, while 3 × 10⁸ claims only one. Both describe the same speed.
Assumptions and limitations
- Rounding works on the digits you typed, and a 5 rounds away from zero. So 1.005 to three significant figures is 1.01.
- E notation uses a lowercase e and no plus sign, as in 2.998e8 and 1.23e-4. Spreadsheets and programming languages accept this form.
- Numbers are stored the standard computer way (as "doubles"). So a number holds at most about 17 significant digits. Sizes are limited to roughly 5 × 10⁻³²⁴ up to 1.8 × 10³⁰⁸.
- This tool changes how a number is written. It doesn't add, subtract, multiply or divide numbers in scientific notation.
Frequently asked questions
What is the difference between scientific and engineering notation?
Scientific notation keeps exactly one digit that isn't zero before the decimal point, so the power can be any whole number. Engineering notation only uses powers that are multiples of 3, matching metric prefixes. So its number in front can be anywhere from 1 up to 999.
How do I tell whether the exponent should be positive or negative?
Numbers of 10 or more have a positive power. Numbers between 0 and 1 have a negative power. A number from 1 up to 10 has a power of 0. The sign of the number itself is separate: −4,500 is −4.5 × 10³.
What does 1.5e-7 mean?
It's E notation for 1.5 × 10⁻⁷. The e stands for "times ten to the power", so 1.5e-7 = 0.00000015. Calculators, spreadsheets and programming languages use it because it fits on one line.
Why does 1200 become 1.20 × 10³ and not 1.2 × 10³?
The zero at the end shows the number was kept to three significant figures, not two. Scientific notation is the clearest way to show precision. 1.2 × 10³, 1.20 × 10³ and 1.200 × 10³ all equal 1,200, but each claims a different accuracy.
How this calculator is checked
Method: Standard definition of normalized scientific notation and engineering notation; significant-figure rounding half away from zero. The calculation is covered by automated tests with known reference values and edge cases. Last updated 2026-10-18. Found a problem? Tell us.
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