Which number in each of the following pairs is smaller? a. 4.9 x 10⁻³ or 5.5 x 10⁻⁹

Scientific notation is a way of expressing numbers that are too large or too small to be conveniently written in decimal form. It is represented as a product of a number (between 1 and 10) and a power of ten. For example, 4.9 x 10⁻³ means 4.9 divided by 1000, which helps in comparing very small or very large values easily.

When comparing numbers in scientific notation, the exponent of ten plays a crucial role. A larger negative exponent indicates a smaller number. For instance, 10⁻³ (0.001) is larger than 10⁻⁹ (0.000000001), meaning that any number multiplied by 10⁻³ will be larger than the same number multiplied by 10⁻⁹, regardless of the coefficients.

To compare numbers in scientific notation directly, converting them to decimal form can be helpful. For example, 4.9 x 10⁻³ converts to 0.0049, while 5.5 x 10⁻⁹ converts to 0.0000000055. This conversion allows for straightforward comparison of the two values, making it easier to determine which is smaller.