Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 1: Problem 36

Perform the following mathematical operations, and express each result to the correct number of significant figures. a. \(\frac{0.102 \times 0.0821 \times 273}{1.01}\) b. \(0.14 \times 6.022 \times 10^{23}\) c. \(4.0 \times 10^{4} \times 5.021 \times 10^{-3} \times 7.34993 \times 10^{2}\) d. \(\frac{2.00 \times 10^{6}}{3.00 \times 10^{-7}}\)

Short Answer

Expert verified
a. \(2.30 \times 10^3\) b. \(8.4 \times 10^{22}\) c. \(2.4 \times 10^4\) d. \(6.67 \times 10^{12}\)

Step by step solution

01

Perform the multiplication operation

First, let's multiply the three numbers in the numerator: \(0.102 \times 0.0821 \times 273\).
02

Correct number of significant figures

As we are multiplying, we should use the least number of significant figures found in the values being multiplied. In this case, the least number of significant figures is 3 (0.102 and 273). Therefore, the result should be expressed with 3 significant figures.
03

Perform the division operation

Now, let's divide the result obtained in step 1 by 1.01.
04

Correct number of significant figures

In a division operation, we again use the least number of significant figures found in the values being divided. In this case, the least number of significant figures is 3 (1.01). So, the final result should be expressed with 3 significant figures. #b. Calculating the expression and applying significant figure rules to the result#
05

Perform the multiplication operation

First, let's multiply the two numbers: \(0.14 \times 6.022 \times 10^{23}\)
06

Correct number of significant figures

As we are multiplying, we should use the least number of significant figures found in the values being multiplied. In this case, the least number of significant figures is 2 (0.14). Therefore, the result should be expressed with 2 significant figures and in scientific notation. #c. Calculating the expression and applying significant figure rules to the result#
07

Perform the multiplication operation

First, let's multiply the three numbers with their respective powers of 10: \(4.0 \times 10^{4} \times 5.021 \times 10^{-3} \times 7.34993 \times 10^{2}\)
08

Correct number of significant figures

As we are multiplying, we should use the least number of significant figures found in the values being multiplied. In this case, the least number of significant figures is 2 (4.0). Therefore, the result should be expressed with 2 significant figures and in scientific notation. #d. Calculating the expression and applying significant figure rules to the result#
09

Perform the division operation

First, let's divide the two numbers in scientific notation: \(\frac{2.00 \times 10^{6}}{3.00 \times 10^{-7}}\)
10

Correct number of significant figures

In a division operation, we again use the least number of significant figures found in the values being divided. In this case, the least number of significant figures is 3 (2.00 and 3.00). So, the final result should be expressed with 3 significant figures and 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.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

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

Explain the fundamental steps of the scientific method.

Sterling silver is a solid solution of silver and copper. If a piece of a sterling silver necklace has a mass of \(105.0 \mathrm{~g}\) and \(\mathrm{a}\) volume of \(10.12 \mathrm{~mL}\), calculate the mass percent of copper in the piece of necklace. Assume that the volume of silver present plus the volume of copper present equals the total volume. Refer to Table \(1.5\). Mass percent of copper \(=\frac{\text { mass of copper }}{\text { total mass }} \times 100\)

Make molecular-level (microscopic) drawings for each of the following. a. Show the differences between a gaseous mixture that is a homogeneous mixture of two different compounds, and a gaseous mixture that is a homogeneous mixture of a compound and an element. b. Show the differences among a gaseous element, a liquid element, and a solid element.

Classify the following mixtures as homogeneous or heterogeneous. a. potting soil b. White wine c. your sock drawer d. window glass e. granite

Round off each of the following numbers to the indicated number of significant digits, and write the answer in standard scientific notation. a. \(0.00034159\) to three digits b. \(103.351 \times 10^{2}\) to four digits c. \(17.9915\) to five digits d. \(3.365 \times 10^{5}\) to three digits
See all solutions

Recommended explanations on Chemistry Textbooks

Kinetics

Read Explanation

Physical Chemistry

Read Explanation

Chemistry Branches

Read Explanation

The Earths Atmosphere

Read Explanation

Chemical Reactions

Read Explanation

Organic Chemistry

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.

Sign-up for free