Standard form (also called scientific notation) is a way of writing very large or very small numbers neatly. A number is in standard form when it is written as a × 10ⁿ, where \(1 \le a < 10\) and n is an integer (a whole number, which can be positive, zero, or negative).

To convert an ordinary number into standard form, start by moving the decimal point so that the first number is between 11 and 1010. Count how many places the decimal point moves. If it moves left, the power of 10 is positive. If it moves right, the power of 10 is negative.

$$
5230000 = 5.23 \times 10^{6}
$$

Here, the decimal point moves 6 places to the left, so the power is 6.

$$
0.0048 = 4.8 \times 10^{-3}
$$

Here, the decimal point moves 3 places to the right, so the power is −3.

To convert from standard form back to an ordinary number, move the decimal point using the power of 10. A positive power means move the decimal point to the right. A negative power means move it to the left.

$$
3.1 \times 10^{4} = 31000
$$

$$
6.2 \times 10^{-2} = 0.062
$$

Always check that the number at the front satisfies \(1 \le a < 10\). If it does not, the number is not in standard form.