Final answer:
The concept discussed here involves rounding two-digit numbers and the use of scientific notation. All digits are considered significant, with particular rules for rounding based on the value of the second digit. This is also related to the simplification of numerical expressions and determining the sign in multiplication and division.
Step-by-step explanation:
The question relates to the process of rounding numbers, which is a fundamental concept in mathematics. When we round a two-digit number, we consider the value of the second digit. If the second digit is 6 or higher, and we need to round to the nearest ten, we round up. This is because all digits in a number are significant. For example, if we look at the number 85, since the second digit (5) is 5 or above, it rounds the 7 up to 8, turning 85 to 90 after rounding. If we have a number like 82, the 2 does not affect the first digit (8), so it remains 80 after rounding.
When using scientific notation, the goal is to simplify the writing of both large and small numbers by having only one non-zero digit to the left of the decimal point. For instance, the number 965 would be written as 9.65 x 10² in scientific notation. This provides a shorthand that makes multiplication and division of such numbers easier to handle.
Moreover, when we multiply or divide numbers, there are specific rules for determining the sign of the result. For example, multiplying two positive numbers results in a positive result, while multiplying numbers with opposite signs results in a negative result.