Scientific Notation Explained: Reading, Writing, and Calculating
October 21, 2026
Scientific notation writes a number as a coefficient between 1 and 10 multiplied by a power of ten: a × 10ⁿ. The speed of light is about 2.998 × 10⁸ meters per second and Avogadro's number is about 6.022 × 10²³. It makes very large and very small numbers compact and easy to compare, and it removes the need to count zeros.
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Open the Scientific Calculator →Converting to and From Scientific Notation
To write a large number, move the decimal point left until one non-zero digit remains in front of it, and count the places moved: 45,000,000 becomes 4.5 × 10⁷. For small numbers, move right and use a negative exponent: 0.00032 becomes 3.2 × 10⁻⁴.
To convert back, shift the decimal point by the exponent: positive exponents move it right, negative ones move it left.
Multiplication and Division
Multiply the coefficients and add the exponents. (3 × 10⁴) × (2 × 10⁵) = 6 × 10⁹. If the coefficient product reaches 10 or more, adjust: (4 × 10³) × (5 × 10²) = 20 × 10⁵ = 2 × 10⁶.
For division, divide the coefficients and subtract the exponents. (6 × 10⁸) ÷ (3 × 10³) = 2 × 10⁵.
Addition and Subtraction
You can only add or subtract once the exponents match. To add 4.5 × 10³ and 2 × 10², rewrite the second as 0.2 × 10³, giving 4.7 × 10³. Alternatively convert both to standard numbers: 4,500 + 200 = 4,700.
A frequent mistake is to add the exponents when adding the numbers. Exponents are added only in multiplication.
E Notation on Calculators
Calculators and programming languages often show 6.022E23 or 6.022e23, which means 6.022 × 10²³. The E stands for exponent and is not the mathematical constant e. A result like 1.5E-3 equals 0.0015.
Scientific notation also communicates precision. Writing 3.50 × 10⁴ tells the reader that the zero is significant, while 3.5 × 10⁴ does not.
Frequently Asked Questions
What is 0.00045 in scientific notation?
4.5 × 10⁻⁴.
How do I multiply numbers in scientific notation?
Multiply the coefficients and add the exponents, then adjust the result so the coefficient is between 1 and 10.
What does E mean on a calculator?
It means 'times ten to the power of'. For instance, 2E5 means 2 × 10⁵, or 200,000.
Why use scientific notation?
It gives a compact, standard way to write extreme values, simplifies calculation, and shows the number of significant figures.