/*! 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 21 Convert each number from scienti... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 21

Convert each number from scientific notation to decimal notation. $$3.667 \times 10^{-3}$$

Short Answer

Expert verified
0.003667

Step by step solution

01

Understanding Scientific Notation

Scientific notation is a shorthand way to write very large or very small numbers. A number in scientific notation has two parts: a decimal part called the coefficient (here, 3.667) and an exponent of 10 (here, -3). The exponent indicates how many places to move the decimal point.
02

Convert to Decimal Notation

Since the exponent is -3, move the decimal point in the coefficient 3 places to the left. If there are not enough digits, add zeros to the left of the number.
03

Writing the Decimal Result

After moving the decimal point three places to the left, the number in decimal notation is 0.003667.

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.

Scientific Notation
Scientific notation is a succinct method to express numbers that are exceptionally large or minuscule. It's composed of a coefficient and a base of 10 raised to an exponent. The coefficient is normally a number between 1 and 10, while the exponent signifies the number of places the decimal point must be shifted. For instance, in the scientific notation \(3.667 \times 10^{-3}\), \(3.667\) is the coefficient and \(-3\) is the exponent. This system is extremely useful in fields like physics and engineering where extreme values are common.
Decimal Notation
Decimal notation is the standard form most people use for writing numbers. It's based on the value of each digit depending on its position, or place value. Converting from scientific to decimal notation involves adjusting the decimal point in a systematic way that reflects the exponent's instruction. When converting the example \(3.667 \times 10^{-3}\) to decimal form, the decimal point moves three places to the left, yielding \(0.003667\). This notation is more familiar in everyday life and foundational in teaching basic mathematics.
Exponents
Exponents are a fundamental mathematical concept that denote the repeated multiplication of a number by itself. The number of times the multiplication is performed is signified by the exponent. When the exponent is positive, it indicates the number of times the base (10 in the case of scientific notation) is multiplied. A negative exponent, such as \(-3\) in the example, implies that the base is divided rather than multiplied, or alternatively, that we're dealing with the reciprocal. So, \(10^{-3}\) equals \(1/10^3\) or \(1/1000\).
Mathematical Concepts
Mathematical concepts provide the building blocks for understanding and working with numbers in diverse ways. Scientific notation and decimal notation exemplify how the same number can be represented differently based on context or utility. Exponents are another layer, allowing concise expression of large numbers or miniscule fractions. It's essential to understand that these concepts aren't isolated but interlinked, forming a cohesive system that mathematicians, scientists, and engineers use to solve real-world problems in a precise and efficient manner.

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

Divide without using a calculator. Give your answer in scientific notation. $$\left(8 \times 10^{4}\right) \div\left(2 \times 10^{2}\right)$$

In the following exercises, substitute the given quantitics into the indicated formula from technology and finance. A bar (Fig. \(1-13\) ) whose length \(L\) is \(15.2 \mathrm{m}\) has a cross- sectional area \(a\) of 12.7 \(\mathrm{cm}^{2} .\) It has an elongation \(e\) of \(2.75 \mathrm{mm}\) when it is subjected to a tensile load of \(22,500 \mathrm{N}\). Use the equation \(E=\frac{P L}{a e}\) to find the modulus of elasticity \(E,\) in newtons per square centimeter.

Multiply without using a calculator. Give your answer in scientific notation. $$\left(5 \times 10^{4}\right)\left(8 \times 10^{-3}\right)$$

8.0 cubic feet of cement is contained in a concrete mixture that is \(12 \%\) cement by volume. What is the volume of the total mixture?

The construction of a building costs \(\$ 136,000\) for materials and \(\$ 157,000\) for labor. What percentage of the total is the labor cost?
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Pure Maths

Read Explanation

Applied Mathematics

Read Explanation

Discrete Mathematics

Read Explanation

Probability and Statistics

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.