Final answer:
In comparing numbers, 3.05 is less than 3.204, -12 is less than -8, and 5/6 is greater than 3/4. These comparisons utilize greater than and less than symbols to concisely represent the relationships between the numbers in question.
Step-by-step explanation:
When comparing numbers and determining whether to use the greater than (>) or less than (<) symbol, we look at the value of the numbers. Let's evaluate each pair:
- A. When comparing 3.05 and 3.204, since the number after the decimal point (3.05 has '05' and 3.204 has '204') for 3.204 is larger, it means that 3.204 is greater. Thus, the correct symbol is 3.05 < 3.204.
- B. For negative numbers, the number that is closer to zero is greater. Since -8 is closer to zero than -12, the correct symbol is -12 < -8.
- C. To compare fractions, we can convert them to a common denominator. The fraction 5/6 is equivalent to 10/12 and 3/4 is equivalent to 9/12. Since 10 is greater than 9, the correct symbol is 5/6 > 3/4.
The use of inequality symbols is crucial when illustrating the relationship between different quantities or expressions. This understanding is foundational in math, whether we're comparing numbers, evaluating the magnitudes of forces, or determining the difference in metric measurements.