Question

When you convert a number from decimal notation to scientific notation, how do you know if the exponent will be positive or negative? Explain.

Answer 1

When converting a number from decimal to scientific notation,

The exponent is positive if the movement of the decimal point is to the left

The exponent is negative if the movement of the decimal point is to the right.

Examples :

$1200\rightarrow1.2\times10^3$

The decimal point moves from the right of the last digit to the place between 1 and 2. It moves to the left so the exponent is positive.

$0.0012\rightarrow1.2\times10^{-3}$

The decimal point will move 3 places to the right, so the exponent will be negative.