/*! 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 86 Convert to decimal notation. $... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 86

Convert to decimal notation. $$ 5.49 \times 10^{-4} $$

Short Answer

Expert verified
0.000549

Step by step solution

01

Understand Scientific Notation

Scientific notation is a way to express very large or very small numbers. In this case, the number is written as \(5.49 \times 10^{-4}\), where 5.49 is the coefficient and \(10^{-4}\) is the power of ten.
02

Interpret the Exponent

The exponent \(-4\) indicates that the decimal point in 5.49 needs to be moved 4 places to the left. This conversion translates the number into standard decimal notation.
03

Shift the Decimal Point

Start with 5.49. Moving the decimal point 4 places to the left, we add zeros as needed: \(0.000549\).
04

Express in Decimal Notation

The final result after shifting the decimal point is \(0.000549\).

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.

Decimal Notation
Decimal notation is a way of writing numbers that uses a decimal point to separate the whole number part from the fractional part. It's the standard way of writing numbers in everyday life, like 123.45 or 0.678. When converting scientific notation to decimal notation, our goal is to express the number without using exponents or powers of ten. For example, converting the number \(5.49 \times 10^{-4}\) into decimal notation involves shifting the decimal point to accurately represent the number.
Exponents
Exponents are used to indicate how many times a number, known as the base, is to be multiplied by itself. In scientific notation, exponents show the power of ten by which the coefficient must be multiplied or divided. For instance, the number \(10^{3}\) means 10 multiplied by itself three times, giving us 1000. Conversely, \(10^{-4}\) indicates a fraction and means the base number should be divided by ten, four times, or equivalently, multiplied by \(0.0001\). In the problem \(5.49 \times 10^{-4}\), the exponent \
Moving the Decimal Point
Scientific notation uses a combination of coefficients and powers of ten to specified the value. The coefficient is the number before the multiplication sign, and it can be any real number. The power of ten indicates how many times the base (10 in this case) needs to be multiplied or divided. For example, in \(5.49 \times 10^{-4}\), 5.49 is the coefficient and \(10^{-4}\) represents a very small number because of the negative exponent. Understanding this combination is key to correctly converting numbers back to decimal notation. It's like a shorthand for dealing with very large or very small numbers in a more manageable way.

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

Simplify. Assume that no denominator is zero and that \(0^{0}\) is not considered. $$ \left(\frac{5 x^{7} y}{-2 z^{4}}\right)^{3} $$

Use the fact that \(10^{3} \approx 2^{10}\) to estimate each of the following powers of \(2 .\) Then compute the power of 2 with a calculator and find the difference between the exact value and the approximation. $$ 2^{31} $$

Replace \(\square\) with \(>,<,\) or \(=\) to write a true sentence. $$ 9^{7} \square 3^{13} $$

For each pair of functions \(f\) and \(g\), determine the domain of \(f / g\) $$ \begin{aligned} &f(x)=5+x\\\ &g(x)=6-2 x \end{aligned} $$

Simplify. Assume that no denominator is zero and that \(0^{0}\) is not considered. $$ \left(\frac{4 x^{3} y^{5}}{3 z^{7}}\right)^{0} $$
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Logic and Functions

Read Explanation

Mechanics Maths

Read Explanation

Pure Maths

Read Explanation

Discrete Mathematics

Read Explanation

Statistics

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.