Question

The radius of Earth is \(6378 . \mathrm{km}\). What is its circumference to three significant figures?

Short answer

Answer: 40000 km

Step-by-step solution

Write down the given information

The radius of Earth is 6378 km.

Apply the circumference formula

Use the formula for the circumference of a circle, which is C = 2πr. In this case, r = 6378 km.

Calculate the circumference

Plug the value of r into the formula and calculate the circumference: C = 2π(6378) km ≈ 40030146.4 km.

Round to three significant figures

Round the calculated circumference to three significant figures: 40030146.4 km ≈ 40000 km.

Write down the final answer

The circumference of Earth to three significant figures is 40000 km.

Key concepts

Circumference Formula

The circumference formula is an essential part of understanding how to measure the distance around a circular object. In mathematics, the circumference of a circle is calculated using the formula: - \( C = 2\pi r \) where:- \( C \) represents the circumference of the circle.- \( \pi \) is a constant, approximately equal to 3.14159.- \( r \) is the radius of the circle.
If you know the radius of a circle, applying the circumference formula allows you to find how far you would travel if you walked around the circle. This is particularly handy for real-world applications, such as determining the Earth's circumference. By knowing the Earth's radius, calculated at 6378 km, you can use the formula to ascertain its circumference.

Significant Figures

Significant figures play a critical role in mathematics and science, ensuring the precision of a calculated value is accurately represented. They communicate the certainty in a measurement and include all known digits plus one estimated digit. When rounding to significant figures, follow these general rules:

• Identify the number of significant figures required.
• Start counting from the first non-zero digit.
• Inspect the digit following your desired number of significant figures to decide whether to round up or maintain the digit.

In our original exercise, we calculate Earth's circumference as 40030146.4 km and then round it to three significant figures. The first three digits are "400," which reflects the rounded figure of the original value. Observing significant figures ensures our mathematical results are both precise and practical.

Mathematics Problem Solving

Mathematics problem solving is a step-by-step method that requires critical thinking and practice. This approach aims to simplify complex equations and real-life problems, translating them into manageable steps:

• Read and understand the problem thoroughly.
• Identify what is required to solve the problem, such as the given and what needs finding.
• Apply relevant formulas or formulas appropriately.
• Perform calculations meticulously to avoid errors.
• Review and round answers as needed.

These steps were employed in our exercise, calculating Earth's circumference. From identifying the radius to applying the circumference formula, and finally rounding the result to significant figures, each step built upon the last to achieve a precise and accurate answer. Through continued practice and dedication, problem solving in mathematics becomes more intuitive and less daunting.