Final answer:
The student's mathematical expressions were evaluated using the order of operations. Additionally, examples were given regarding how to express calculations in scientific notation with the correct significant figures.
Step-by-step explanation:
The student has asked to evaluate the following mathematical expressions:
- (25 + 5) × 3 - 13
- 12 + 34 × 2 ÷ 2
- 4^3 - (2 + 2^3) × 5
- (9 - 3)^2 + 5 ÷ 1/3
Let's solve each of them step by step using the order of operations (PEMDAS/BODMAS): parentheses, exponents, multiplication and division (from left to right), and addition and subtraction (from left to right).
- 90 - 13 = 77
- 12 + 68 = 80
- 64 - (2 + 8) × 5 = 64 - 10 × 5 = 64 - 50 = 14
- (6)^2 + 5 ÷ 3 = 36 + 15 = 51
The student is also asked to express certain calculations in scientific notation with the appropriate number of significant figures. For example:
- 217 ÷ 903 = 0.2403, which is approximately 2.403 × 10^-1 in scientific notation.
- 13.77 + 908.226 + 515 = 1,437.996, which is approximately 1.438 × 10^3 in scientific notation.
- 255.0 - 99 = 156.0, which is 1.560 × 10^2 in scientific notation.
- 0.00666 × 321 = 2.13786, which is approximately 2.138 × 10^0 in scientific notation.