Final answer:
The student asked a Mathematics question about division, involving large numbers and verifying if the quotients presented were correct. Significant figures are crucial in obtaining a precise quotient, and calculators often give more decimal places than what is significant, which can lead to inaccuracies.
Step-by-step explanation:
The question involves the mathematical concept of division, which relates to the terms dividend, divisor, and quotient. In the given examples, large values are divided, and one must verify if the resulting quotients are correct. Here's a breakdown of these terms:
- Dividend: The number being divided.
- Divisor: The number by which the dividend is divided.
- Quotient: The result of the division.
When dividing, the process involves subtracting the exponent of the divisor from that of the dividend if in scientific notation. It is crucial to account for significant figures when dividing, especially when using calculators, as they often provide more decimals than significant in the numbers being calculated, leading to inaccuracies.
Here's how you would check the first example:
- Identify the dividend (5674) and the divisor (82).
- Divide 5674 by 82 using long division or a calculator.
- Verify if the quotient obtained is 69.
In a practical sense, when considering significant figures, the quotient should contain no more digits than that in the factor having the least number of significant figures. As per the examples provided and the rules of significant figures, handling large numbers necessitates the care for accuracy and the understanding of concepts like scientific notation and significant figures.