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Chapter 1: Problem 14

What is an exponent? How are exponents used in powers-often notation?

Short Answer

Expert verified
An exponent indicates how many times a number (the base) is used in a multiplication. Exponents are used in powers-of-ten notation to provide a compact way of representing large or small numbers, where the base is always 10. For instance, 3000 can be represented as \(3*10^3\), and 0.002 as \(2*10^{-3}\).

Step by step solution

01

Defining an Exponent

An exponent refers to the number of times a number, known as the base, is used in a multiplication. It is denoted in the form \(a^n\), where \(a\) is the base and \(n\) is the exponent. For instance, in \(2^3\), 2 is the base and 3 is the exponent; this expression means 2 is multiplied by itself 3 times i.e., \(2*2*2\).
02

Powers-of-Ten Notation

Exponents are particularly used in powers-of-ten notation to represent large or small numbers succinctly. In powers-of-ten notation, the base is always 10. For instance, \(10^3\) means the number 10 is multiplied by itself 3 times to give 1000. This simplifies the representation of large (or small) numbers. For instance, 3000 can be represented as \(3*10^3\) and 0.002 as \(2*10^{-3}\).
03

Use of Exponents and Powers-of-Ten notation

Exponents and powers-of-ten notation are widely used in various fields such as physics, engineering, and computer science to represent very large or very small numbers in a compact form. By understanding how to use them, problems involving large or small numbers can be solved more conveniently.

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Most popular questions from this chapter

Look up at the sky on a clear, cloud-free night and note the positions of a few prominent stars relative to such reference markers as rooftops, telephone poles, and treetops. Also note the location from where you make your observations. A few hours later, return to that location and again note the positions of the same bright stars that you observed earlier. How have their positions changed? From these changes, can you deduce the general direction in which the stars appear to be moving?

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