Question

A teacher selected 8 students at random and asked them to write numbers in scientific notation on notecards. The teacher asked all the students in the classroom to determine who wrote the number with the least value and wrote the number with the most value.

Answer 1

Scientific notation is a mathematical method to express very large or very small numbers through a coefficient and a power of 10. It simplifies comparing and working with such numbers by focusing on the exponents and coefficients to determine their relative values.

Step-by-step explanation:

The scientific notation is utilized in mathematics to express extremely large or small numbers in a more manageable form. It consists of a coefficient and a power of 10. The coefficient is the number after adjusting the decimal point so it is at least 1 but less than 10, followed by the remaining significant figures.

The power of 10 is determined by the number of places the decimal point has moved to convert between the standard and scientific notation forms. As an example, the number 79,345 in scientific notation is expressed as 7.9345 × 10⁴ since the decimal point has been moved four places to the left.

To decide which student wrote the smallest or largest number, students should compare the exponents first. If the exponents are the same, then they should compare the coefficients. Whichever number has the smallest exponent or coefficient is the smallest value, and conversely, the largest exponent or coefficient would indicate the largest value in scientific notation.

Answer 2

Scientific notation is a mathematical method used to express very large or small numbers by a coefficient and a power of 10. Students can compare the values on their notecards by looking at the coefficients and exponents, where the least and most values are determined by the smallest and largest exponents respectively.

Step-by-step explanation:

The subject matter revolves around scientific notation, a mathematical method used to write very large or very small numbers succinctly. In scientific notation, a number is expressed as a product of a coefficient and a power of 10. The coefficient is a number between 1 and 10, and the power of 10 represents how many times the coefficient needs to be multiplied by 10 to achieve the original number. For instance, 79,345 in scientific notation is written as 7.9345 × 104.

To determine the numbers with the least and most value among the students' notecards, one would compare their coefficients and exponents. The smallest value would likely have the smallest exponent or a smaller coefficient in cases with same exponents. Conversely, the largest value would have the largest exponent or a larger coefficient in cases with the same exponents. Scientific notation is especially useful in subjects such as physics or chemistry where extreme values are common.