Round each of the following numbers to four significant figures and express the result in standard exponential notation: (a) 102.53070

Verified step by step guidance

1. Identify the number of significant figures required: In this case, it is four significant figures.
2. Locate the fourth significant figure in the original number 102.53070. Counting from the first non-zero digit, the fourth significant figure is 2.
3. Check the digit immediately after the fourth significant figure, which is 5. Since it is 5 or greater, round up the fourth significant figure by one.
4. After rounding, the number becomes 102.6.
5. Express the rounded number in standard exponential notation: $1.026 \times 10^2$.

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 calculations.

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 standard numbers into scientific notation is important for clarity and ease of calculation in chemistry.