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Chapter 1: Problem 15

What are the advantages of using powers-of-ten notation?

Short Answer

Expert verified
Advantages of using powers-of-ten notation include: convenient representation of very large or small numbers, simplification of calculations involving these numbers, accurate signaling of significant figures, and better comparison of different scales.

Step by step solution

01

Understand the Concept of Powers-of-Ten

Powers-of-ten notation, also known as scientific notation, is a way to write very large or very small numbers using bases and exponents. A number written in powers-of-ten notation is written as a product of a number between 1 and 10 and a power of 10.
02

Explain the Usefulness in Writing Large or Small Numbers

Expressing large numbers, such as the distance from Earth to the nearest galaxy or small numbers such as the size of an atom, in standard form can be unwieldy and lead to errors. Powers-of-ten notation provides a concise and precise way to represent these types of numbers.
03

Describe the Simplification in Calculations

Calculations involving multiplication, division, addition, and subtraction become much simpler with powers-of-ten notation. For example, when we multiply two powers of 10, we can simply add the exponents. Similarly, when dividing, we subtract the exponents.
04

Explain the Advantage in Signaling Significant Figures

Scientific notation also assists in indicating the number of significant figures in a number. The digits in the digit part (the number between 1 and 10) are the significant figures.
05

Showcase the Ease in Scale Comparison

Powers-of-ten notation allows for easier comparison of scales. For instance, when comparing population sizes or atomic sizes, it's much easier to comprehend the difference in magnitude when numbers are written using powers-of-ten notation.

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Most popular questions from this chapter

The average distance to the Moon is \(384,000 \mathrm{~km}\), and the Moon subtends an angle of \(1 / 2^{\circ}\). Use this information to calculate the diameter of the Moon in kilometers.

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