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Chapter 10: Problem 15

For Exercises \(13-20,\) write each power of 10 in exponential notation. $$1000$$

Short Answer

Expert verified
1000 in exponential notation is \(10^3\).

Step by step solution

01

Understand the Problem

The goal is to write the number 1000 in exponential notation using a base of 10.
02

Identify the Base

The base of our exponential notation is 10.
03

Count the Zeros

The number 1000 can be written as 1 followed by three zeros.
04

Write in Exponential Notation

Since the number 1000 is 1 followed by three zeros, it can be written as 10 raised to the power of 3. Thus, the exponential notation is \(10^3\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Powers of 10
A 'power of 10' refers to any number that can be expressed as 10 raised to an exponent. In simpler terms, it's 10 multiplied by itself a certain number of times. For example, 1000 is a power of 10 because it is equal to 10 multiplied by itself three times. This can be written as \(10^3\). Each power of 10 is composed of a '1' followed by a number of zeros equal to the exponent. For instance:
  • \(10^1 = 10\)
  • \(10^2 = 100\)
  • \(10^3 = 1000\)
  • \(10^4 = 10000\)
Understanding the powers of 10 helps in simplifying large numbers and making mathematical operations more intuitive.
Exponents
Exponents tell us how many times a number, known as the 'base,' is multiplied by itself. In the expression \(10^3\), 10 is the base and 3 is the exponent. This indicates that 10 is multiplied by itself three times: \(10 \times 10 \times 10 = 1000\). Exponents have the following parts:
  • The base: The number that is going to be raised to a power, for instance, 10 in \(10^3\).
  • The exponent: The small number placed to the upper right of the base, showing how many times to multiply the base by itself, for instance, 3 in \(10^3\).
Using exponents makes it easier to write and work with large numbers. Instead of writing out all the zeros, you can express them with a base and exponent.
Mathematics Education
Mathematics education involves teaching and learning key math concepts and skills, ranging from basic arithmetic to advanced calculus. Understanding exponents and powers of 10 is foundational in math education because they:
  • Simplify complex calculations
  • Help in scientific notation
  • Are used in various scientific and engineering fields
To improve your understanding, it's helpful to:
Practice by writing numbers in both standard and exponential notation
Use visual aids like number lines or charts
Engage in interactive exercises that challenge your comprehension
Learning these concepts deeply helps build confidence and competence in mathematics.

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Most popular questions from this chapter

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