Scientific Notation: How to Write Massively Large and Small Numbers

Instantly convert any massive number into a standardized E-notation format using our Scientific Notation Converter, or read on to learn the manual math formatting rules.

The universe is full of extremes. The mass of the Earth is approximately 5,970,000,000,000,000,000,000,000 kilograms. The mass of an electron is approximately 0.00000000000000000000000000000091 kilograms.

Writing, reading, and doing math with all of those zeros is prone to massive errors. To solve this, scientists developed Scientific Notation, a standardized method of writing numbers as a product of a decimal and a power of 10.

The Rules of Scientific Notation

A number written in proper scientific notation always follows a strict, two-part format: a × 10^b

1. The Coefficient (a): This must be a number strictly greater than or equal to 1, and strictly less than 10. (e.g., 5.97 or 9.1).
2. The Base-10 Exponent (b): This tells you how many places to move the decimal point. A positive exponent means the number is very large (move decimal right). A negative exponent means the number is very small (move decimal left).

Converting Large Numbers

Let's convert the distance from the Earth to the Sun: 93,000,000 miles.

1. Place a decimal point so the coefficient is between 1 and 10: 9.3
2. Count how many places you moved the decimal point from the end of the original number to its new spot. We moved it 7 places to the left.
3. The exponent is positive 7.

Answer: 9.3 × 10^7

Converting Small Numbers

Let's convert the size of a red blood cell: 0.000008 meters.

1. Move the decimal point to the right until you have a number between 1 and 10: 8.0
2. Count how many places you moved the decimal point. We moved it 6 places to the right.
3. Because the original number was a fraction of 1, the exponent is negative 6.

Answer: 8.0 × 10^-6

E-Notation on Calculators

If you type a massive calculation into your phone or a standard calculator, you might see a result that looks like this: 3.45E8.

Because physical calculators and computer keyboards don't always support superscript formatting for exponents (like 10⁸), computer scientists developed E-Notation.

In E-Notation, the "E" simply stands for "Exponent of 10."

• 3.45E8 is exactly the same as 3.45 × 10^8.
• 1.2E-4 is exactly the same as 1.2 × 10^-4.

Calculating with Scientific Notation

The beauty of scientific notation is that it makes multiplication and division incredibly simple by using the rules of exponents.

Multiplying: Multiply the coefficients together, and add the exponents together. (2 × 10^3) × (3 × 10^4)

• Coefficients: 2 × 3 = 6
• Exponents: 3 + 4 = 7
• Answer: 6 × 10^7

Dividing: Divide the coefficients, and subtract the exponents. (8 × 10^5) / (2 × 10^2)

• Coefficients: 8 / 2 = 4
• Exponents: 5 - 2 = 3
• Answer: 4 × 10^3

FAQ

Why does the coefficient have to be less than 10? Standardization. Technically, 45.0 × 10^3 and 4.5 × 10^4 represent the exact same value (45,000). But to ensure that scientists globally write numbers uniformly, the rule strictly dictates that the coefficient must be a single digit followed by a decimal.

---

Formatting complex physics equations is tedious. Format your data perfectly into Standard or E-Notation using the CalcUnit Scientific Notation Converter.