Final answer:
The correct order of precedence is exponents, multiplication/division, and addition/subtraction, often remembered by the acronym PEMDAS. In scientific notation, multiplication and division involve combining coefficients and adding or subtracting exponents, following sign rules.
Step-by-step explanation:
The correct order of precedence for mathematical symbols is exponents, multiplication/division, and finally addition/subtraction. This is often remembered using the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction), indicating the sequence in which operations should be performed in a mathematical expression. When dealing with scientific notation, operations such as multiplication and division simplify because you can directly multiply or divide the leading numbers (N) and add or subtract their exponents (n).
For example, in multiplying two numbers in scientific notation, we follow these steps:
- Multiply the coefficients (N).
- Add the exponents (n).
For division, the process is:
- Divide the coefficients (N).
- Subtract the exponents (n).
When considering multiplication and division, remember that the sign rules apply: multiplying or dividing two numbers with the same sign results in a positive number, while doing so with numbers of opposite signs results in a negative number.