Final answer:
The expression (6.67×10⁻¹¹)×(7.36×10²²)/(1.73×10⁶)² can be rewritten as 16.4×10⁻¹ when expressed in scientific notation following rules for multiplying and dividing powers of ten and rounding to three significant figures.
Step-by-step explanation:
The question involves rewriting the expression (6.67×10⁻¹¹)×(7.36×10²²)/(1.73×10⁶)² using the properties of scientific notation. The process involves multiplying and dividing the given numbers in scientific notation to obtain the final expression in the same format.
To rewrite the expression, we'll start by handling the numerator and the denominator separately. In scientific notation, when multiplying powers of ten, you add the exponents. Conversely, when dividing powers of ten, you subtract the exponents. Here's the step-by-step process:
- Multiply the coefficients (numbers in front of the powers of ten) of the numerator: 6.67 × 7.36 to get 49.1312.
- Add the exponents in the numerator: (-11) + 22 = 11, so we have 49.1312×10¹¹.
- Square the denominator's coefficient: (1.73) ² = 2.9929.
- Double the exponent in the denominator since it's squared: (6) × 2 = 12.
- Divide the coefficient of the numerator by the coefficient of the denominator: 49.1312 / 2.9929 ≈ 16.4232.
- Subtract the exponent of the denominator from the exponent of the numerator: 11 - 12 = -1.
- Combine the final coefficient and exponent to express the answer in scientific notation: 16.42 × 10⁻¹ (rounded to three significant figures).
So the rewritten expression in scientific notation, limited to three significant figures, is 16.4 × 10⁻¹.