/*! 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 55 Express each number in decimal n... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 55

Express each number in decimal notation. \(7.86 \times 10^{-4}\)

Short Answer

Expert verified
The number \(7.86 \times 10^{-4}\) in decimal notation is \(0.000786\).

Step by step solution

01

Recognize the number in scientific notation

The number \(7.86 \times 10^{-4}\) is in scientific notation. Scientific notation is a way of expressing numbers that are too large or too small to be conveniently written in decimal form. It takes the form \(a \times 10^n\), where \(1 鈮� |a| < 10\) and n is an integer.
02

Understand the exponent

The exponent in our number is \(-4\). This means we will move the decimal towards the left, because a negative exponent means 'divide by' and division by a factor of ten decreases the size of the number.
03

Move the decimal

We begin moving the decimal point 4 places to the left, because the exponent is \(-4\). Since there are less than 4 places after decimal in \(7.86\), we add zeros in necessary places. Therefore, after moving 4 places left, we get the number in decimal notation as \(0.000786\).

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 the standard way of writing numbers using base 10. It is the number format we're most familiar with in everyday life. This system uses ten symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. Most importantly, it arranges numbers using place value. Each position in a number has a value ten times that of the position to its right.
For example, in the number 345, the 5 represents 5 units, the 4 represents 40 (or four tens), and the 3 represents 300 (or three hundreds).
  • Decimals, like 0.786, express values less than one using fractional parts, written to the right of the decimal point.
  • With decimal notation, we can express whole numbers, fractions, and exact values efficiently and precisely.

Converting from scientific to decimal notation involves adjusting the decimal point based on the exponent provided in the scientific notation.
Negative Exponents
Negative exponents occur when numbers are raised to a power less than zero. When dealing with powers of ten, a negative exponent means you are essentially dividing by ten a specific number of times. For example, in the expression \(10^{-4}\), the negative exponent indicates that you divide by ten four times, resulting in \(0.0001\).
  • A simple way to think of negative exponents is that they 'invert' the number. Thus, \(10^{-n}\) becomes \(\frac{1}{10^n}\).
  • This can be useful for expressing very small quantities in a manageable form without writing many zeros.

Understanding negative exponents is crucial when shifting the decimal place in scientific notation, as each decrement in value shrinks the number.
Number Conversion
Number conversion refers to the process of changing a number from one form to another, without changing its value. This concept encompasses converting between decimal, fraction, and scientific notations. In the context of scientific notation, you must be comfortable with shifting the decimal point based on the exponent value.
  • For positive exponents, shift the decimal point to the right.
  • For negative exponents, shift the decimal to the left.
  • Each movement corresponds to either multiplying or dividing by ten.

To convert \(7.86 \times 10^{-4}\) to decimal notation, recognize that the negative exponent signals a leftward shift. Simply move the decimal left four places to get \(0.000786\). This fundamental skill of converting numbers ensures accurate representation and comparison across diverse mathematical 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

Determine whether each statement makes sense or does not make sense, and explain your reasoning. I've noticed that the big difference between arithmetic and geometric sequences is that arithmetic sequences are based on addition and geometric sequences are based on multiplication.

Enough curiosities involving the Fibonacci sequence exist to warrant a flourishing Fibonacci Association. It publishes a quarterly journal. Do some research on the Fibonacci sequence by consulting the research department of your library or the Internet, and find one property that interests you. After doing this research, get together with your group to share these intriguing properties.

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. A sequence that is not arithmetic must be geometric.

The bar graph shows changes in the percentage of college graduates for Americans ages 25 and older from 1990 to \(2015 .Involve developing arithmetic sequences that model the data. In \)1990,24.4 \%\( of American men ages 25 and older had graduated from college. On average, this percentage has increased by approximately \)0.3\( each year. a. Write a formula for the \)n\(th term of the arithmetic sequence that models the percentage of American men ages 25 and older who had graduated from college \)n\( years after \)1989 .\( b. Use the model from part (a) to project the percentage of American men ages 25 and older who will be college graduates by \)2029 .$

Write the first six terms of the geometric sequence with the first term, \(a_{1}\), and common ratio, \(r\). \(a_{1}=-6, r=-5\)
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Pure Maths

Read Explanation

Applied Mathematics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Decision Maths

Read Explanation

Discrete Mathematics

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.