The diameter of the Earth at the equator is 7926.381 mi. (b) Express the answers in scientific notation.

Verified step by step guidance

1. Identify the given value: The diameter of the Earth at the equator is 7926.381 miles.
2. Understand scientific notation: A number is expressed in scientific notation as \( a \times 10^n \), where \( 1 \leq a < 10 \) and \( n \) is an integer.
3. Convert the given number to scientific notation: Move the decimal point in 7926.381 to the left until only one non-zero digit remains to the left of the decimal.
4. Count the number of places the decimal point was moved: This will determine the exponent \( n \) in the scientific notation.
5. Express the number in scientific notation: Combine the adjusted number with the power of ten, \( 10^n \), to complete the conversion.

Key Concepts

Scientific Notation

Scientific notation is a method of expressing numbers that are too large or too small in a compact form. It is written as a product of a number between 1 and 10 and a power of ten. For example, the number 7926.381 can be expressed as 7.926381 x 10^3 in scientific notation, simplifying calculations and comparisons.

Significant Figures

Significant figures are the digits in a number that contribute to its precision. This includes all non-zero digits, any zeros between significant digits, and trailing zeros in the decimal portion. When converting to scientific notation, it is important to maintain the correct number of significant figures to ensure the accuracy of the representation.

Unit Conversion

Unit conversion involves changing a quantity expressed in one unit to another unit while maintaining the same value. In this context, understanding the diameter of the Earth in miles may require converting to kilometers or other units for different scientific applications. However, the question specifically asks for the expression in scientific notation, so unit conversion is not necessary here.