/*! 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 106 Perform the indicated computatio... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 0: Problem 106

Perform the indicated computations. Write the answers in scientific notation. If necessary, round the decimal factor in your scientific notation answer to two decimal places. $$\frac{66,000 \times 0.001}{0.003 \times 0.002}$$

Short Answer

Expert verified
The output is \(1.1 \times 10^7\).

Step by step solution

01

Perform multiplication

Firstly, perform the multiplications: \(66,000 \times 0.001 = 66\); \(0.003 \times 0.002 = 0.000006\)
02

Perform Division

Next, divide the two products: \(66 梅 0.000006\). That equals \(11000000\).
03

Convert to Scientific Notation

Finally, convert that big number to scientific notation. The number \(11000000\) can be written as \(1.1 \times 10^7\) in scientific notation.

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.

Multiplication
Multiplication is a fundamental arithmetic operation that is often used when working with scientific notation. To multiply numbers, you essentially add together equal groups of something. For example, multiplying 66,000 by 0.001 means you are taking 66,000 items and creating 0.001 equal groups, which in simpler terms means scaling down the number significantly. In this exercise, you multiply:
  • 66,000 and 0.001 to get 66
  • Then, multiply 0.003 by 0.002 to get 0.000006
These results will then help you with the next step, which involves division.
Division
Division is the process of splitting a quantity into equal parts or groups. It's the arithmetic operation that separates a number into a specified number of parts. In the given exercise, you divide the products of the multiplication step. Here's how you perform the division:
  • Take 66 (from the first multiplication result)
  • Divide it by 0.000006 (from the second multiplication result)
This division yields the result of 11,000,000. You may notice this produces a very large number, which can be conveniently expressed in scientific notation.
Decimal Places
Decimal places refer to the number of digits to the right of the decimal point in a number. Rounding to a specified number of decimal places can simplify calculations and improve readability. In scientific notation, it may be necessary to round the decimal factor. For the exercise, when rounding is mentioned, consider how it affects the precision of your number. In our division result of 11,000,000, there are no digits after the decimal, but when converting to scientific notation, precision might demand rounding the leading decimal number if there were trailing digits (e.g., 1.123 to 1.12). In this problem, the conversion simplifies to 1.1 which rounds to two decimal places.
Convert to Scientific Notation
Scientific notation is a method for expressing numbers that are too big or too small to conveniently write in decimal form. It鈥檚 expressed as a product of a number (the mantissa) and a power of ten.To convert a number like 11,000,000:
  • Identify the first non-zero digit, which is 1
  • Count how many places are moved to position the decimal after 1, which is 7 places
  • Express the number as a product: 1.1 (rounded) times 10 to the power of 7, so we write it as \(1.1 \times 10^7\).
This method makes it easier to read and work with large numbers, particularly in scientific and engineering contexts.

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

Exercises \(159-161\) will help you prepare for the material covered in the next section. In parts (a) and (b), complete each statement. a. \(\frac{b^{7}}{b^{3}}=\frac{b \cdot b \cdot b \cdot b \cdot b \cdot b \cdot b}{b \cdot b \cdot b}=b^{2}\) b. \(\frac{b^{8}}{b^{2}}=\frac{b \cdot b \cdot b \cdot b \cdot b \cdot b \cdot b \cdot b}{b \cdot b}=b^{?}\) c. Generalizing from parts (a) and (b), what should be done with the exponents when dividing exponential expressions with the same base?

Use the strategy for solving word problems, modeling the verbal conditions of the problem with a linear inequality. A city commission has proposed two tax bills. The first bill requires that a homeowner pay \(\$ 1800\) plus \(3 \%\) of the assessed home value in taxes. The second bill requires taxes of \(\$ 200\) plus \(8 \%\) of the assessed home value. What price range of home assessment would make the first bill a better deal?

Explain how to determine the restrictions on the variable for the equation $$\frac{3}{x+5}+\frac{4}{x-2}=\frac{7}{x^{2}+3 x-6}$$

Will help you prepare for the material covered in the first section of the next chapter. If \(y=4-x,\) find the value of \(y\) that corresponds to values of \(x\) for each integer starting with \(-3\) and ending with 3

The bar graph shows the percentage of U.S. college freshmen with an average grade of A in high school. (GRAPH CAN NOT COPY) The data displayed by the bar graph can be described by the mathematical model $$p=\frac{4 x}{5}+25$$ where \(x\) is the number of years after 1980 and \(p\) is the percentage of U.S. college freshmen who had an average grade of A in high school. Use this information a. According to the formula, in 2010 , what percentage of U.S. college freshmen had an average grade of \(A\) in high school? Does this underestimate or overestimate the percent displayed by the bar graph? By how much? b. If trends shown by the formula continue, project when \(57 \%\) of U.S. college freshmen will have had an average grade of A in high school.
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Statistics

Read Explanation

Pure Maths

Read Explanation

Probability and Statistics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Mechanics Maths

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.