/*! 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 84 Express the given number in scie... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 8: Problem 84

Express the given number in scientific notation. $$0.00431$$

Short Answer

Expert verified
The scientific notation for 0.00431 is \(4.31 \times 10^{-3}\).

Step by step solution

01

Identify the Significant Figures

Determine the significant figures in the provided number. In 0.00431, the significant figures are 4, 3, and 1.
02

Move the Decimal Point

Move the decimal point to the right of the first significant digit to form a new number between 1 and 10. For 0.00431, moving the decimal point 3 places to the right gives 4.31.
03

Count the Number of Moves

Count how many places you moved the decimal point. For 0.00431, the decimal point was moved 3 places to the right.
04

Adjust the Exponent

Since the decimal point was moved to the right, the exponent will be negative. Use the number of places you moved the decimal point as the exponent. Thus, the exponent is -3.
05

Write in Scientific Notation

Combine the number between 1 and 10 with the power of 10. The scientific notation for 0.00431 is written as \(4.31 \times 10^{-3}\).

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
Significant figures are the digits in a number that carry meaningful information about its precision. In the context of scientific notation, significant figures help us understand the accuracy of the measurement. To determine the significant figures in a number, count all digits starting from the first non-zero digit.

In the number 0.00431, the significant figures are 4, 3, and 1. These digits give us precise information about the value's true accuracy.

Proper identification of significant figures is crucial for correct scientific notation, as it shows the precision of the measured value.
decimal point
The decimal point is used to separate the integer part of a number from its fractional part. When converting a number to scientific notation, one of the key steps involves moving the decimal point to a position immediately to the right of the first significant figure.

For instance, in the number 0.00431, you move the decimal point three places to the right, making it 4.31. This adjustment helps transform the number into a value between 1 and 10, which is a necessary condition for scientific notation.

The final position of the decimal point determines the exponent's value in scientific notation.
exponent
The exponent in scientific notation indicates how many places the decimal point was moved to convert the number into a value between 1 and 10. This exponent is written as a power of 10.

If you move the decimal point to the right, the exponent will be negative. Conversely, if you move it to the left, the exponent will be positive. For example, moving the decimal point three places to the right in 0.00431 results in an exponent of -3.

Thus, the scientific notation for 0.00431 becomes 4.31 脳 10^{-3}. The exponent simplifies the notation and makes it easier to handle very large or very small numbers.

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

Factor each of the following as completely as possible. If the expression is not factorable, say so. Try factoring by grouping where it might help. $$3 x^{2} y+6 x y-5 x-10$$

Use scientific notation to compute each of the following. $$\frac{(2,400)(0.003)}{(0.02)(0.004)}$$

Simplify the expression and express your final answer with positive exponents only. $$\frac{\left(x^{-2} y^{3}\right)^{-1}}{\left(x^{3}\right)^{-2}}$$

Factor each of the following expressions as completely as possible. If an expression is not factorable, say so. $$c^{2}-13 c+12$$

Factor each of the following as completely as possible. If the expression is not factorable, say so. Try factoring by grouping where it might help. $$y^{2}+w y-7 y-7 w$$
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Logic and Functions

Read Explanation

Statistics

Read Explanation

Discrete Mathematics

Read Explanation

Calculus

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.