Scientific Notation: How to Convert Numbers

Scientific notation writes any number in the form a x 10^n, where a is at least 1 but less than 10, and n is a whole-number exponent. It's a compact way to handle very large or very small values. For example, 4500 becomes 4.5 x 10^3, and 0.0032 becomes 3.2 x 10^-3. You can convert in either direction with our free scientific notation converter.

The form: a x 10^n

The number a is called the coefficient, and it must satisfy 1 is less than or equal to the absolute value of a, which is less than 10 — so exactly one non-zero digit sits in front of the decimal point. The exponent n tells you how many places the decimal point moved, and in which direction. A positive exponent means a large number; a negative exponent means a small one.

Big numbers: a positive exponent

Move the decimal point to the left until just one non-zero digit remains in front of it, and count the moves. For 4500, the decimal moves three places left to land on 4.5, so 4500 = 4.5 x 10^3. The exponent 3 is positive because the original number is bigger than the coefficient.

COSMIQ — Home — COSMIQ landing page

Small numbers: a negative exponent

For numbers smaller than 1, move the decimal point to the right until one non-zero digit sits in front of it, and count those moves as a negative exponent. For 0.0032, the decimal moves three places right to reach 3.2, so 0.0032 = 3.2 x 10^-3.

Converting back to standard form

To undo scientific notation, move the decimal the number of places the exponent indicates: right for a positive exponent, left for a negative one. So 6.02 x 10^2 = 602, and 1.5 x 10^-2 = 0.015. Adding zeros as placeholders when you run out of digits is completely normal.

Convert with confidence

When you want a quick, accurate conversion in either direction, use the scientific notation converter, and to keep your precision honest, pair it with the significant figures calculator. To have the why explained out loud, COSMIQ's free voice tutor is free for every learner.

COSMIQ — About COSMIQ