Final answer:
The student's question contains unclear elements with potential typos, making it challenging to provide a precise answer. For evaluating expressions in scientific notation, follow rules of significant figures and operations with powers of ten. In scientific notation, express numbers with a single non-zero digit to the left of the decimal, multiplied by a power of 10.
Step-by-step explanation:
The student's question seems to be a combination of different math problems, some of which involve evaluating expressions and working with powers. However, the formatting of the student's question is unclear, and it seems there may be some typos, which make it difficult to provide an accurate answer without further clarification. Nonetheless, based on the relevant information provided, we can explore some of the concepts related to scientific notation, significant figures, and powers of 10.
Evaluating expressions in Scientific Notation
To evaluate expressions using scientific notation, one must follow several rules regarding significant figures and operations with powers of ten. When multiplying powers of 10, for example, the exponent values are added together.
Example:
- (4.506 × 10^4) × (1.003 × 10^2) can be computed by adding the exponents since the base is the same (10). The result would be 4.506 × 1.003 × 10^(4+2), which equals approximately 4.513518 × 10^6 when accounting for significant figures.
Expressing Numbers in Scientific and Standard Notation
To express numbers in notation, place a single non-zero digit to the left of the decimal point, then multiply by a power of 10 that shifts the decimal to its original location. To convert to standard notation, move the decimal point the number of places indicated by the exponent.
Examples:
- 7.11 × 10^-2 in standard notation is 0.0711.
- 1.381 × 10^-23 in standard notation is 0.00000000000000000000001381.