Calculate to the correct number of significant figures. c. (9443 + 45 - 9.9) × 8.1 × 106

Verified step by step guidance

1. insert step 1: Begin by performing the operations inside the parentheses: 9443 + 45 - 9.9.
2. insert step 2: Determine the number of significant figures for the result of the operation inside the parentheses. The number with the least decimal places is 9.9, which has one decimal place.
3. insert step 3: Perform the multiplication with 8.1. The number 8.1 has two significant figures.
4. insert step 4: Multiply the result by 106. The number 106 has three significant figures.
5. insert step 5: The final result should be rounded to the least number of significant figures from the multiplication steps, which is two significant figures from 8.1.

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 count and apply significant figures is crucial for ensuring that calculations reflect the precision of the measured values.

Order of Operations

The order of operations is a set of rules that dictates the sequence in which calculations should be performed to ensure accurate results. The common acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) helps remember this order. Applying these rules correctly is essential for solving mathematical expressions accurately.

Dimensional Analysis

Dimensional analysis is a method used to convert units and ensure that equations are dimensionally consistent. It involves using conversion factors to relate different units and can help in verifying that calculations yield results in the desired units. This concept is particularly useful in chemistry for ensuring that quantities are expressed correctly in terms of their physical dimensions.