Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 2: Problem 80

Do these calculations using a scientific calculator and report your answers in scientific notation: (a) \(\left(3.33 \times 10^{4} \mathrm{~km}\right)+\left(2.22 \times 10^{5} \mathrm{~km}\right)\) (b) \(\left(2.444 \times 10^{9} \mathrm{~J}\right) \div\left(2.444 \times 10^{-9} \mathrm{~J}\right)\) (c) \(\left(2.34 \times 10^{2} \mathrm{~m}\right)-\left(2.34 \times 10^{1} \mathrm{~m}\right)\) (d) \(\left(4.00 \times 10^{4} \mathrm{~L}\right)+\left(6.00 \times 10^{-1} \mathrm{~L}\right)\)

Short Answer

Expert verified
(a) \(2.553 \times 10^5\) km (b) \(1 \times 10^{18}\) (c) \(2.106 \times 10^2\) m (d) \(4.006 \times 10^4\) L

Step by step solution

01

Align the exponents

To add the numbers, we need to have the same exponent. Here, we will rewrite \(3.33 \times 10^4\) as \(0.333 \times 10^5\).
02

Add the numbers with the same exponent

Now that we have the same exponent, we can add the mantissas together: \(0.333 + 2.22 = 2.553\).
03

Write the result in scientific notation

The final result is \(2.553 \times 10^5\) km. (b) $\left(2.444 \times 10^{9} \mathrm{~J}\right) \div\left(2.444 \times 10^{-9} \mathrm{~J}\right)$
04

Divide the mantissas

We need to divide the mantissas: \(\frac{2.444}{2.444} = 1\).
05

Subtract the exponents

After dividing the mantissas, we need to subtract the exponents: \(9 - (-9) = 18\).
06

Write the result in scientific notation

The final result is \(1 \times 10^{18}\). (c) $\left(2.34 \times 10^{2} \mathrm{~m}\right)-\left(2.34 \times 10^{1} \mathrm{~m}\right)$
07

Align the exponents

To subtract the numbers, we need to have the same exponent. Here, we will rewrite \(2.34 \times 10^1\) as \(0.234 \times 10^2\).
08

Subtract the numbers with the same exponent

Now that we have the same exponent, we can subtract the mantissas: \(2.34 - 0.234 = 2.106\).
09

Write the result in scientific notation

The final result is \(2.106 \times 10^2\) m. (d) $\left(4.00 \times 10^{4} \mathrm{~L}\right)+\left(6.00 \times 10^{-1} \mathrm{~L}\right)$
10

Align the exponents

To add the numbers, we need to have the same exponent. Here, we will rewrite \(6.00 \times 10^{-1}\) as \(0.006 \times 10^4\).
11

Add the numbers with the same exponent

Now that we have the same exponent, we can add the mantissas together: \(4.00 + 0.006 = 4.006\).
12

Write the result in scientific notation

The final result is \(4.006 \times 10^4\) L.

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

Two students measure the density of gold. One works with a \(100-g\) bar of pure gold. The other works with a \(200-g\) bar of pure gold. Which student measures the larger density? Explain your answer.

A microscopic particle is measured and found to have a \(40.2\) micron diameter. What is its diameter in meters? What is its diameter in nanometers?

Why is it necessary for a calorimeter to be insulated?

Which one of the following expresses the measured value \(1230.0 \mathrm{~m}\) with the correct number of significant figures and appropriate Greek prefix? (a) \(1.23 \mathrm{~km}\) (b) \(1.230 \mathrm{~cm}\) (c) \(1.2300 \mathrm{~km}\) (d) \(1.2300 \mathrm{~mm}\) (e) \(12.3 \mathrm{~km}\)

For solids, the amount of material per unit volume is often expressed in grams per milliliter, whereas for gases the amount of material per unit volume is usually expressed in grams per liter. If the amount of matter in air is \(1.34 \mathrm{~g} / \mathrm{L}\), what is this value in: (a) \(\mathrm{g} / \mathrm{mL}\) (b) \(\mathrm{kg} / \mathrm{L}\) (c) \(\mathrm{kg} / \mathrm{mL}\) ?
See all solutions

Recommended explanations on Chemistry Textbooks

Kinetics

Read Explanation

Making Measurements

Read Explanation

Chemical Analysis

Read Explanation

Chemical Reactions

Read Explanation

Nuclear Chemistry

Read Explanation

The Earths Atmosphere

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