Round each of the following numbers to four significant figures and express the result in standard exponential notation: (e) −0.0357202.

Verified step by step guidance

1. Identify the number of significant figures required: In this case, it is four significant figures.
2. Locate the first non-zero digit in the original number, −0.0357202. The first non-zero digit is 3.
3. Count four significant figures starting from the first non-zero digit. The four significant figures are 3572.
4. Round the number based on the digit following the fourth significant figure. Since the digit following 2 is 0, the number remains 3572.
5. Express the rounded number in standard exponential notation: −0.03572 can be written as −3.572 \times 10^{-2}.

Key Concepts

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. Understanding how to identify and round significant figures is crucial for accurately reporting measurements in scientific contexts.

Rounding Rules

Rounding rules dictate how to adjust numbers to a specified number of significant figures. When rounding, if the digit following the last significant figure is 5 or greater, the last significant figure is increased by one. If it is less than 5, the last significant figure remains unchanged. Mastery of these rules is essential for precise numerical representation.

Scientific Notation

Scientific notation is a method of expressing numbers as a product of a coefficient and a power of ten, which simplifies the representation of very large or very small numbers. In this format, the coefficient is typically a number between 1 and 10. Understanding how to convert numbers into scientific notation is important for clarity and ease of calculation in chemistry.