In Exercises 77–86, write each number in scientific notation. −0.00000000405

Key Concepts

Scientific Notation

Scientific notation is a way of expressing numbers that are too large or too small in a compact form. It is written as the product of a number between 1 and 10 and a power of ten. For example, the number 4,500 can be expressed as 4.5 × 10^3. This notation simplifies calculations and comparisons of very large or very small values.

Negative Exponents

Negative exponents indicate that the base number should be divided rather than multiplied. For instance, 10^-3 means 1 divided by 10 raised to the power of 3, or 1/1000. In scientific notation, negative exponents are often used to represent very small numbers, such as 0.00000405, which can be expressed as 4.05 × 10^-9.

Significant Figures

Significant figures are the digits in a number that contribute to its precision. This includes all non-zero digits, any zeros between significant digits, and trailing zeros in the decimal portion. When converting to scientific notation, it is important to maintain the correct number of significant figures to accurately represent the original number's precision, such as ensuring that 4.05 retains its significant figures when expressed as 4.05 × 10^-9.