Understand, convert, and calculate with scientific notation — the standard way to express very large and very small numbers.
Scientific notation is a compact way to write numbers that are extremely large or extremely small. Instead of writing 602,214,076,000,000,000,000,000 (the number of molecules in 18 grams of water), you write 6.022 × 10²³. This system is used universally in science, engineering, computing, and finance. In this guide, you will learn exactly how scientific notation works, how to convert numbers in both directions, how to perform calculations, and when to use it. For instant conversions, check out our free scientific notation converter.
Scientific notation expresses a number in the form:
where:
A positive exponent means a large number; a negative exponent means a small number. The key idea is that scientific notation captures both the precision (through the coefficient) and the magnitude (through the exponent) of a number.
Move the decimal point to the left until only one non-zero digit remains to the left of it. The number of places you moved becomes the exponent.
Move the decimal point to the right until one non-zero digit is to the left of it. The number of places becomes a negative exponent.
To convert back to standard form, move the decimal point in the direction indicated by the exponent's sign.
(3 × 10⁴) × (2 × 10³)
(8.4 × 10⁶) / (2.1 × 10²)
(3.2 × 10⁵) + (1.8 × 10⁴)
In computing and on many calculators, scientific notation is written using E notation. The "E" (or "e") stands for "exponent" and replaces the "× 10" part:
E notation is used because it is easier to type on a keyboard and is universally understood by programming languages, spreadsheets, and scientific calculators. When you see a number like 1.5e10 in a spreadsheet, it means 1.5 × 10¹⁰ (15 billion).
Engineering notation is a variant where the exponent is always a multiple of 3 (..., −6, −3, 0, 3, 6, ...). This aligns with SI prefixes like milli (10⁻³), kilo (10³), mega (10⁶), and giga (10⁹), making it especially useful in engineering and electronics. For example, 47,000 Ω becomes 47 × 10³ Ω (47 kΩ) in engineering notation.
Scientific notation makes it easy to express significant figures (also called significant digits). The coefficient shows the precision of the measurement. Writing 3.00 × 10⁶ indicates three significant figures (the measurement is precise to the nearest ten thousand), while 3 × 10⁶ indicates only one significant figure (the measurement is precise only to the nearest million).
This distinction is critical in scientific work — it communicates the reliability and precision of your data.
Our free scientific notation converter handles any number in both directions — plus E notation and engineering notation.
Yes. The coefficient can be negative to represent negative numbers. For example, −5.2 × 10³ = −5,200. The rule 1 ≤ |a| < 10 applies to the absolute value of the coefficient.
Scientific notation requires the coefficient to be between 1 and 10 with any integer exponent. Engineering notation requires the exponent to be a multiple of 3, which means the coefficient can range from 1 to 999.
Most calculators have an "EE" or "EXP" button. To enter 3.2 × 10⁵, press 3.2, then EE or EXP, then 5. Some calculators use the E notation display directly.
No — the coefficient must be between 1 and 10. The correct form is 5 × 10². Similarly, 15 × 10³ is incorrect and should be written as 1.5 × 10⁴.
Use more decimal places in the coefficient. For example, 9.1093837015 × 10⁻³¹ kg represents the electron mass to 12 significant figures. The more digits in the coefficient, the more precise the value.
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