/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 72 Evaluate each expression. Round ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 72

Evaluate each expression. Round off your answer to the nearest thousandth where necessary. $$(1.83)^{5}$$

Short Answer

Expert verified
19.444

Step by step solution

01

- Understanding the Problem

The exercise asks to evaluate the expression \( (1.83)^5 \). This means you need to multiply 1.83 by itself five times.
02

- Calculate the Expression

Calculate the power of the number by multiplying 1.83 by itself five times. Using a calculator, compute \( (1.83)^5 \).
03

- Perform the Calculation

Using a calculator, \( (1.83)^5 \) results in approximately 19.4442982783.
04

- Round to the Nearest Thousandth

Round the answer to the nearest thousandth. The number 19.4442982783 rounded to the nearest thousandth is 19.444.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

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

Evaluating Expressions
Evaluating expressions is a fundamental part of algebra. In this exercise, we evaluated the expression \( (1.83)^5 \). This involves calculating the value by raising the base number (1.83) to the power of 5.
To understand evaluations, remember:
  • The base (1.83 in this case) is the number being multiplied.
  • The exponent (5) tells you how many times to multiply the base by itself.
So, \( (1.83)^5 \) means 1.83 multiplied by itself five times: 1.83 * 1.83 * 1.83 * 1.83 * 1.83.
Accurate calculation often requires a calculator, especially when dealing with large exponents.
Rounding Numbers
Rounding numbers makes them simpler and easier to use. You often round to a specific decimal place for consistency. In this exercise, we rounded to the nearest thousandth.
Here鈥檚 how to round to the nearest thousandth:
  • Identify the digit in the thousandth place. In 19.4442982783, it's the third digit after the decimal: 鈥�4鈥�.
  • Look at the digit right after it. If it's 5 or more, round up the thousandth digit by 1. Otherwise, leave it as is.
For 19.4442982783, the thousandth digit is 4 and the next digit is 2 (less than 5). Therefore, rounded to the nearest thousandth, it stays 19.444.
Using a Calculator
Using a calculator is essential for complex calculations, especially in algebra. Here鈥檚 how to use a calculator effectively:
  • Enter the base number correctly: Type 1.83.
  • Use the exponent function (often labeled as \(^ \) or \( y^x \)): Type ^ or tap the exponent button.
  • Enter the exponent: Type 5. Then press 'equals' or 'compute' to get the result.
For \( (1.83)^5 \), the calculator should display approximately 19.4442982783. Using a calculator simplifies the process and increases accuracy, especially with large or precise values.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Simplify by combining like terms whenever possible. $$y^{2}-6 y+y^{2}-y$$

Simplify by combining like terms whenever possible. $$0.18 x+0.25(72-x)$$

Simplify each expression as completely as possible. $$4(y-3)-2[3 y-5(y-1)]$$

Evaluate the given expression for \(x=2, y=-3,\) and \(z=-4.\) $$(x y)^{2}-(x-y)^{2}$$

Evaluate the given expression for \(x=0.24\) and \(y=-0.5 .\) Round off to the nearest thousandth where necessary. $$8.4 x-0.03 y$$
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Logic and Functions

Read Explanation

Applied Mathematics

Read Explanation

Discrete Mathematics

Read Explanation

Mechanics Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.