(b) The circumference of Earth through the poles is 40,008 km. Round this number to four significant figures and express it in standard exponential notation.

Verified step by step guidance

1. Identify the number of significant figures required, which is four in this case.
2. Round the given number, 40,008 km, to four significant figures. This involves looking at the first four digits and rounding based on the fifth digit.
3. After rounding, express the number in standard exponential notation. This involves writing the number as a product of a number between 1 and 10 and a power of 10.
4. Determine the power of 10 by counting how many places the decimal point has moved from the original number to the new number in standard form.
5. Combine the rounded number and the power of 10 to express the final result in standard exponential notation.

Key Concepts

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 rounding a number, it is essential to retain the correct number of significant figures to accurately represent the precision of the measurement.

Rounding Rules

Rounding rules dictate how to adjust a number to a specified number of significant figures. If the digit immediately following the last significant figure is 5 or greater, the last significant figure is increased by one. If it is less than 5, the last significant figure remains unchanged. This process ensures that the rounded number is as close as possible to the original value.

Standard Exponential Notation

Standard exponential notation expresses numbers as a product of a coefficient and a power of ten. This format is useful for simplifying large or small numbers, making them easier to read and compare. For example, the number 40,008 can be expressed as 4.0008 x 10^4 in standard exponential notation, where the coefficient is between 1 and 10.