Question

Height of Mt. Everest The height of Mt. Everest is 8848 meters. \(^{*}\) Express this height in scientific notation.

Short answer

8.848 × 10³

Step-by-step solution

Understanding Scientific Notation

Scientific notation is a way of expressing numbers that are too big or too small to be conveniently written in decimal form. It is expressed as the product of a number (usually between 1 and 10) and a power of 10.

Write the Number in Decimal Form

Start by writing down the height of Mt. Everest in decimal form: 8848.

Identify the Significant Figures

The number 8848 has four significant figures: 8, 8, 4, and 8.

Convert the Number to a Form Between 1 and 10

Move the decimal point in 8848 to the left until only one non-zero digit remains to the left of the decimal point. This converts 8848 to 8.848.

Determine the Power of 10

Count the number of places the decimal point was moved. In this case, the decimal point was moved 3 places to the left, which equals to multiplying by 10³.

Combine the Parts

Combine the significant figures (8.848) with the power of 10 (10³). Therefore, 8848 in scientific notation is written as 8.848 × 10³.

Key concepts

significant figures

Significant figures are crucial in scientific calculations. They tell us how precise a number is. The number 8848 has four significant figures: 8, 8, 4, and 8. When we convert to scientific notation, we must keep all these significant figures to maintain accuracy. Ignoring significant figures can lead to incorrect results in scientific measurements and calculations. In our case of 8848, identifying all four significant figures ensures that our final scientific notation, 8.848 × 10³, remains accurate and precise.

decimal form

Numbers are typically written in decimal form, which has digits followed by a decimal point. Expressing Mt. Everest's height in decimal form is straightforward: it's 8848. Decimal form is useful, but it becomes cumbersome with extremely large or small numbers. This is why we use scientific notation—to simplify representation without losing precision. By writing 8848 as 8.848 × 10³, it becomes easier to read and manage, especially in scientific contexts.

power of 10

The power of 10 in scientific notation indicates how many times the number should be multiplied by ten. When converting a number like 8848, we move the decimal point 3 places to the left, giving us a power of 3. This transformation is represented as 10³. Powers of 10 are essential in scientific notation because they help convert any number to a standardized form that is easier to read and work with, especially in very large or small numbers.

expressing large numbers

Expressing large numbers like the height of Mt. Everest can be challenging in traditional decimal form. Scientific notation helps by simplifying the representation. By converting 8848 to 8.848 × 10³, we make it easier to handle. This is particularly useful in science and engineering, where we frequently deal with extremely large or small measurements. Understanding how to express large numbers in this concise format can help you tackle complex calculations with ease.