/*! 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 97 In Exercises \(91-106\), write e... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 97

In Exercises \(91-106\), write each number in scientific notation. $$6751$$

Short Answer

Expert verified
The scientific notation of 6751 is \(6.751 \times 10^3\).

Step by step solution

01

Identify the decimal point

The decimal point in an integer is not shown, but it is always to the right of the last digit. So in this case, the decimal point for 6751 is after the 1.
02

Move the decimal point

Move the decimal point to the left so it is after the first number. Count the number of places you've moved it - in this case, it is 3 places. This gives us 6.751.
03

Write in scientific notation format

We write this in the form \(a \times 10^n\) where \(1 \leq a < 10\) and n is an integer. The value a is found by moving the decimal place, and n is the number of places the decimal was moved. Since we moved the decimal place to the left, n is positive. Therefore, the scientific notation for 6751 is \(6.751 \times 10^3\).

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 Point
In any number, the decimal point is an important concept that denotes where the fractional part of a number begins. For a whole number, like 6751, the decimal point might not be visible. However, it is understood to be right after the last digit of the integer.
For example, in 6751, although we don't write it, the decimal point is actually present as 6751.0. This implied decimal point is crucial when you want to convert numbers into scientific notation.
  • When converting an integer to scientific notation, you need to move this hidden decimal point to balance the equation format.
  • Typically, you'll move the decimal to the left for whole numbers.
  • The number of moves determines the exponent in your scientific notation.
Understanding where the decimal point is gives you the starting position for converting to scientific notation effectively.
Integer
An integer is a whole number that can be positive, negative, or zero, but it doesn't have any fractional parts. In our problem, 6751 is an integer because it consists only of whole units with no decimals or fractions involved.

  • Since integers do not normally show a decimal point, it's important to understand its implicit location for scientific notation.
  • Converting an integer to scientific notation involves recognizing its structure as a series of digits that, when combined with a hidden decimal, can form a base number.
  • The value represented by an integer provides the baseline for moving the decimal point and determining the power of ten used.
Recognizing and working with integers is an essential step in accurately expressing them in scientific notation.
Positive Exponent
A positive exponent in scientific notation signifies how many times you multiply the number by 10. It's like scaling up the number because you're moving the decimal point a certain number of places to the left.
For the number 6751, when converting to scientific notation, the decimal point is moved 3 places to the left to make the base number between 1 and 10, which gives us 6.751.

Understanding Exponents

- If you moved the decimal point to the left, the exponent is positive, indicating multiplication by powers of 10. - A positive exponent: 6.751 becomes 6751 due to being multiplied by 10 raised to the power of 3.
  • The number of places the decimal point is moved directly gives the exponent value.
  • Positive exponents make the number larger, aligning with the original integer value.
Knowing how a positive exponent affects the number is key to mastering scientific notation.

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. Each statement applies to the division problem $$\frac{x^{3}+1}{x+1}$$ The purpose of writing \(x^{3}+1\) as \(x^{3}+0 x^{2}+0 x+1\) is to keep all like terms aligned.

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. When a certain polynomial is divided by \(2 x+4,\) the quotient is $$x-3+\frac{17}{2 x+4}$$ What is the polynomial?

What is the degree of a polynomial? Provide an example with your explanation.

Divide each expression using the quotient rule. Express any numerical answers in exponential form. $$\frac{x^{200} y^{40}}{x^{25} y^{10}}$$

determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. The number of people who catch a cold \(t\) weeks after January 1 is \(5 t-3 t^{2}+t^{3}\) The number of people who recover \(t\) weeks after January 1 is \(t-t^{2}+\frac{1}{3} t^{3}\) Write a polynomial in standard form for the number of people who are still ill with a cold \(t\) weeks after January 1
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Statistics

Read Explanation

Applied Mathematics

Read Explanation

Mechanics Maths

Read Explanation

Probability and Statistics

Read Explanation

Theoretical and Mathematical Physics

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.