/*! 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 1 Convert each number into scienti... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 7: Problem 1

Convert each number into scientific notation. $$4530$$

Short Answer

Expert verified
4.530 脳 10^3

Step by step solution

01

- Identify Significant Figures

The significant figures in the number 4530 are 4, 5, 3, and 0.
02

- Place Decimal Point

To convert to scientific notation, place the decimal point after the first significant figure: 4.530
03

- Count the Exponent

Count the number of places the decimal point has moved. The decimal point moved 3 places to the left.
04

- Write in Scientific Notation

Combine the significant figures with the power of ten based on the number of places moved: \[ 4.530 \times 10^3 \]

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.

significant figures
Understanding significant figures is essential in scientific notation. Significant figures are the digits in a number that contribute to its precision. For 4530, the significant figures are 4, 5, 3, and 0. Be aware that zeroes can be tricky; they are only significant if they are between other significant digits or at the end of a number with a decimal point.

By identifying significant figures, we ensure accuracy when expressing numbers in scientific notation. Knowing which digits are significant helps in converting large or small numbers into a more manageable form.
decimal point
The placement of the decimal point is crucial when converting numbers to scientific notation. In regular notation, the position of the decimal point helps define the value of the number. For converting 4530, we place the decimal point after the first significant figure, transforming it to 4.530.

This step ensures that the number is properly scaled between 1 and 10 in scientific notation. Notice how the location of the decimal point changes the look but not the value of the number. By moving the decimal point, we adjust the exponent accordingly, leading to the power of ten needed to represent the original number.

In this example, the decimal moved 3 places to the left.
exponent
The exponent in scientific notation shows how many places the decimal point has moved to form a number between 1 and 10. For the number 4530, after placing the decimal point to get 4.530, we see it has moved 3 spaces to the left.

The exponent tells us the power of ten needed to scale the number back to its original form. In this case, it's \[ 4.530 \times 10^3 \]. The exponent of 3 indicates that the decimal point moved 3 places, reflecting the original magnitude of the number.

This helps in simplifying and accurately communicating very large or very small numbers in fields such as science, engineering, and mathematics.

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

Multiply out each of the following. As you work out the problems, identify those exercises that are either a perfect square or the difference of two squares. $$(2 y+5)(4 y-3)$$

Multiply out \((x+6)(x+4)\) and \((x-6)(x-4) .\) What is the effect of switching both \(+\) signs to \(-\) signs?

Multiply out each of the following. As you work out the problems, identify those exercises that are either a perfect square or the difference of two squares. $$(2 y+3)(y-5)$$

A certain sum of money is invested at \(10 \%,\) and twice that amount is invested at \(12 \% .\) If the annual interest from the two investments is \(\$ 408,\) how much is invested at each rate?

In this section we defined \(a^{0}=1 .\) It is important to realize that a definition is neither right nor wrong-it just is. The proper question to ask about a definition is "Is it useful?" What happens if someone decides on an "alternative definition" such as \(a^{0}=7\) because 7 happens to be his or her favorite number? What happens when we consider the expression \(a^{0} \cdot a^{4} ?\) If you use exponent rule 1 you get \(a^{0} \cdot a^{4}=a^{0+4}=a^{4} .\) However, if you use this alternative definition, you get \(a^{0} \cdot a^{4} \stackrel{\underline{2}}{=} 7 a^{4} .\) The answer we get from the alternative definition is not consistent with the answer we get from the exponent rule. The exponent rules and this alternative definition cannot coexist. Since we do not want to throw away all the exponent rules, we must modify the alternative definition so that it is consistent with all the exponent rules. Verify that our definition of \(a^{0}=1\) is consistent with all five exponent rules.
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Mechanics Maths

Read Explanation

Discrete Mathematics

Read Explanation

Calculus

Read Explanation

Pure Maths

Read Explanation

Applied 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.