/*! 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 76 Perform the indicated operations... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 8: Problem 76

Perform the indicated operations. $$3.5 \times 1,000$$

Short Answer

Expert verified
The product of multiplying 3.5 by 1,000 is 3,500.

Step by step solution

01

Understand the Multiplication

In this exercise, you need to multiply the numbers 3.5 and 1,000 to find the product. This means you will find how much 3.5 groups of 1,000 is in total.
02

Apply Basic Multiplication Rules

Multiply 3.5 by 1,000. When multiplying a decimal by a power of 10, you can move the decimal point to the right by the number of zeros in the power of 10. Since 1,000 has 3 zeros, move the decimal in 3.5 three places to the right.
03

Perform the Calculation

Start with 3.5. Move the decimal point three places to the right. After moving, since there's only one digit after the decimal point and we need to move three, add 2 zeros at the end of 35 to accommodate the move. This gives us 3,500.

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.

Understanding Decimal Point Movement
When multiplying decimal numbers, especially by powers of ten, understanding how the decimal point moves is crucial. In the exercise, we multiplied 3.5 by 1,000. Here, the decimal point movement plays an essential role in simplifying the process. To move the decimal point, look at the number of zeros in the factor鈥搒ince 1,000 has three zeros, move the decimal point in 3.5 three places to the right.
  • Start with 3.5, which is written as 3.5.
  • Moving it one place changes it to 35 (3.5 becomes 35.0).
  • Continue moving it two more places to get 3,500.
Always remember to fill any empty decimal places with zeros if necessary. This ensures that the number retains its magnitude as required by its multiplication.
Grasping Powers of Ten
Powers of ten are fundamental in performing efficient multiplication and division with decimals. Each power represents how many times to multiply 10 by itself, like 10, 100, 1,000, and so on. In our example, multiplying by 1,000 means we use 10 raised to the power of 3. Here鈥檚 how it works:
  • Power of zero (100) is 1.
  • Power of one (101) is 10.
  • Power of two (102) is 100.
  • Power of three (103) is 1,000.
The exponents indicate how many zeros are added when multiplied by 10. Therefore, 1,000 signifies that 3 zeros will be added when adjusting the decimal point, which transforms 3.5 into 3,500 effortlessly.
Mastering Basic Multiplication Rules with Decimals
Basic multiplication rules apply in decimal multiplication similarly to whole numbers, but with a focus on handling the decimal point. Follow these steps to ensure accuracy:
  • Ignore the decimal point initially and multiply the numbers as if they were whole numbers.
  • After finding the product, correctly place the decimal point. In our exercise, shift it based on the powers of ten rule.
For example, with 3.5 x 1,000:
  • Consider 35 and 1,000 as the numbers.
  • 35 x 1,000 equals 35,000.
  • Adjust for decimals: Moving the point three places right leads to the product 3,500.
By sticking to these steps, you'll effectively handle decimal multiplications without error.

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

Perform the indicated operations. $$1.5 \times 30$$

Set up the following problems as you have been doing. Then use a calculator to perform the actual calculations. Round answers to two decimal places where appropriate. The engine of a car has a displacement of 440 cubic inches. What is the displacement in cubic feet?

Perform the indicated operations. $$15+60$$

Set up the following problems as you have been doing. Then use a calculator to perform the actual calculations. Round answers to two decimal places where appropriate. Convert \(7,362\) fl oz to gallons.

Perform the indicated operations. $$73-60$$
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Decision Maths

Read Explanation

Mechanics Maths

Read Explanation

Statistics

Read Explanation

Probability and Statistics

Read Explanation

Logic and Functions

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.