Final answer:
In high school mathematics, it is essential to express answers with the correct number of significant figures and proper units. Significant figures provide precision in mathematical answers, while proper units are required for clear communication of the quantity measured. Always follow the specific instructions given in the question for significant figures and units.
Step-by-step explanation:
When expressing the answers to problems in mathematics, especially in high school level physics or chemistry, it is critical to pay attention to significant figures and proper units. Significant figures are the digits in a number that are known with a certain degree of reliability and contribute to its precision. Proper units, on the other hand, are the standardized measurement indicating the quantity of the answer, such as meters, grams, or seconds. To express your answer with the correct number of significant figures, follow these rules:
- All nonzero digits are significant.
- Zeros between nonzero digits are significant.
- Leading zeros before the first nonzero digit are not significant.
- Trailing zeros in a decimal number are significant.
- Trailing zeros in a whole number with a decimal are significant, but in a whole number without an explicitly written decimal point, they may not be deemed significant.
For example, if you were calculating the area of a rectangle and you got an answer of 123.40 square meters, the answer would have five significant figures because all the digits, including the trailing zero after the decimal point, are significant.
Expressing proper units alongside your answer is also crucial. When performing any calculation, be sure to carry the units through every step and express your final answer with the appropriate unit. If you are calculating distance and the answer comes out to 5400 meters for instance, stating '5400 m' clearly communicates both the numerical value and the measurement scale used.
Lastly, when providing answers, always reflect upon the instructions given in the question regarding the expected significant figures and units. This practice ensures that your answer adheres to the standards required by the context of the question.