Final answer:
To create and evaluate a numerical expression with parentheses, exponents, and operations, select numbers, use operations addition or multiplication, include parentheses for order, apply an exponent, and then evaluate. For example, (4² + 2) ÷ 3 equals 6. Use proper significant figures and scientific notation when necessary.
Step-by-step explanation:
To create and evaluate your own numerical expression using parentheses, exponents, and at least two operations, you can follow these steps:
- Choose numbers to use in your expression. For example, let's select 4 and 2.
- Decide on the operations you wish to use such as addition, subtraction, multiplication, or division.
- Use parentheses to establish the order of operations. Remember that anything inside the parentheses is calculated first.
- Include an exponent to elevate a number to a power.
- Write down the complete numerical expression. An example could be: (4² + 2) ÷ 3.
- Now, evaluate the expression step-by-step:
The result of the expression (4² + 2) ÷ 3 is 6.
It's important to express your answers to problems with the correct number of significant figures and proper units. In this case, our numbers are all integers, so significant figures are not a primary concern, and no specific units are involved.
When working with more complex problems, especially in scientific contexts, expressing numbers in scientific notation can be useful, particularly when dealing with very large or small numbers. Scientific notation allows for easier arithmetic operations and comparison of magnitudes. For example, expressing the number 5,000 in scientific notation would be 5 × 10³.
To ensure thorough understanding, it is recommended to write down these calculations rather than just reading them. Also, when adding or subtracting numbers in scientific notation, make sure all the exponents have the same value before performing the operation.