Calculate to the correct number of significant figures. a. [(1.7×10⁶) / (2.63×10⁵)] + 7.33 b. (568.99 - 232.1) / 5.3

Verified step by step guidance

1. Identify the operations involved: multiplication and addition.
2. Perform the multiplication: \((1.7 \times 10^6) \times (2.63 \times 10^5)\).
3. Determine the number of significant figures for the multiplication result. The number with the fewest significant figures is 1.7 (2 significant figures).
4. Add the result of the multiplication to 7.33. Ensure the addition is done with the correct number of decimal places based on the least precise measurement.
5. Express the final result with the correct number of significant figures, considering both the multiplication and addition steps.

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.

Scientific Notation

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. This notation simplifies calculations, especially when dealing with very large or small quantities, which is common in chemistry.

Order of Operations in Calculations

The order of operations is a set of rules that dictates the sequence in which calculations should be performed to ensure accurate results. In chemistry, this typically follows the PEMDAS/BODMAS rule (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). Correctly applying this order is essential when performing calculations involving addition, especially when combining numbers in scientific notation.