Calculate to the correct number of significant figures. b. (5.01×10⁵) / (7.8×10²)

Verified step by step guidance

1. Identify the numbers involved in the calculation: 5.01 \times 10^5 and 7.8 \times 10^2.
2. Determine the number of significant figures in each number: 5.01 has 3 significant figures and 7.8 has 2 significant figures.
3. Perform the division: (5.01 \times 10^5) / (7.8 \times 10^2).
4. Calculate the result of the division without rounding yet.
5. Round the final result to the least number of significant figures from the original numbers, which is 2 significant figures.

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 significant figures is crucial for accurately reporting measurements and calculations in chemistry, as it reflects the precision of the data used.

Multiplication and Division Rules for Significant Figures

When performing multiplication or division, the result should be reported with the same number of significant figures as the measurement with the least number of significant figures. This rule ensures that the precision of the result is not overstated, maintaining the integrity of the data derived from the calculations.

Scientific Notation

Scientific notation is a way of expressing numbers that are too large or too small in a more manageable form, using powers of ten. In the context of the given question, it allows for easier multiplication and division of numbers by simplifying the process of handling significant figures and ensuring clarity in the representation of very large or small quantities.