/*! 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 38 For Exercises \(35-42,\) multipl... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 38

For Exercises \(35-42,\) multiply the numbers by the powers of 10 and \(0.1 .\) $$18.22 \times 1000$$

Short Answer

Expert verified
18220.

Step by step solution

01

Identify the initial value

The initial value given is 18.22.
02

Identify the power of 10

The number is to be multiplied by 1000, which is a power of 10. Specifically, 1000 can be represented as 10^3.
03

Move the decimal point

When multiplying by 10^3 (1000), move the decimal point 3 places to the right. The initial value is 18.22. By moving the decimal point three places, we get 18220.

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.

Decimal Point Movement
When you multiply a number by a power of 10, you essentially shift the decimal point. The number of places you move the decimal point corresponds to the exponent. If the exponent is positive, you move the decimal point to the right. For example, multiplying 18.22 by 1000 (which is equivalent to multiplying by 10^3) means you move the decimal point three places to the right. Therefore, 18.22 becomes 18220.

This concept not only applies to positive powers but to negative ones as well. If you were dividing by 1000 or multiplying by 0.001, you would move the decimal point three places to the left.
Powers of Ten
Understanding powers of ten is crucial in mathematics. A power of ten refers to 10 raised to an exponent. For beginners, here are some basics:
  • 10^1 = 10
  • 10^2 = 100
  • 10^3 = 1000

The exponent tells you how many zeros follow the 1. Powers of ten make large and small numbers easier to work with. Multiplying by a power of ten essentially scales a number up or down by moving the decimal point, making arithmetic operations simpler.
Scientific Notation
Scientific notation is a method for expressing very large or very small numbers. It uses powers of ten to simplify these numbers. In this format, a number is written as:
\[ a \times 10^n \]

where 'a' is a number greater than or equal to 1 but less than 10, and 'n' is an integer.

For instance, the number 18220 can be written in scientific notation as 1.822 x 10^4. This approach makes it easier to handle large computations and understand the order of magnitude of the number.
Basic Arithmetic Operations
Basic arithmetic operations include addition, subtraction, multiplication, and division. Multiplication involves combining groups of a number, making it essential for understanding how to scale values. When multiplying by powers of ten, you're adding these groups exponentially.
  • Addition: 18220 + 5000 = 23220
  • Subtraction: 18220 - 5000 = 13220
  • Multiplication: 18.22 脳 1000 = 18220
  • Division: 18220 梅 1000 = 18.22

Mastery of these operations is fundamental to more advanced topics in math.

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

Olivia's diet allows her 60 grams (g) of fat per day. If she has \(\frac{1}{4}\) of her total fat grams for breakfast and a McDonald's Quarter Pounder \((20.7\) g of fat) for lunch, how many grams does she have left for dinner?

Water flows into a pool at a constant rate. The water level is recorded at several 1-hr intervals. a. From the table, how many inches is the water level rising each hour? b. At this rate, what will the water level be at 1: 00 PM.? c. At this rate, what will the water level be at 3.00 p.M.? $$\begin{array}{c|c} \text { Time } & \text { Water Level } \\ \hline 9: 00 \mathrm{A} . \mathrm{M} & 4.2 \mathrm{in} . \\ \hline 10: 00 \mathrm{A} \ldots & 5.9 \mathrm{in} . \\ \hline 11.00 \mathrm{A} \ldots & 7.6 \mathrm{in} . \\ \hline 12.00 \mathrm{em} . & 9.3 \mathrm{in.} \\ \hline \end{array}$$

An outdoor torch lamp shines light a distance of \(30 \mathrm{ft}\) in all directions. What is the total ground area lighted?

For Exercises \(85-90,\) refer to the table. The table gives the closing stock prices (in dollars per share) for the first day of trading for the given month. $$\begin{array}{l|c|c|c|c|c} \text { Stock } & \text { January } & \text { February } & \text { March } & \text { April } & \text { May } \\ \hline \text { IBM } & \$ 97.27 & \$ 99.00 & \$ 92.27 & \$ 95.21 & \$ 103.17 \\\ \hline \text { FedEx } & \$ 109.77 & \$ 111.89 & \$ 114.16 & \$ 106.07 & \$ 106.11 \\ \hline \end{array}$$ Between which two consecutive months did the FedEx stock increase the most? What was the amount of increase?

What is the greatest number with three places to the right of the decimal that can be created from the digits 2, 9, and 7? Assume that the digits cannot be repeated.
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Decision Maths

Read Explanation

Logic and Functions

Read Explanation

Statistics

Read Explanation

Pure Maths

Read Explanation

Geometry

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.