/*! 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 13 Write each number in scientific ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Problem 13

Write each number in scientific notation. $$ 0.00000692 $$

Short Answer

Expert verified
6.92 脳 10^{-6}

Step by step solution

01

- Identify the Significant Figures

First, identify the significant figures in the number 0.00000692. These are the digits that contribute to the precision of the number: 6, 9, and 2.
02

- Move the Decimal Point

Move the decimal point to the right of the first significant figure (6 in this case) to form a new number between 1 and 10. After moving the decimal point, we get 6.92.
03

- Count the Decimal Places Moved

Count the number of places you moved the decimal point to reach 6.92. In this case, the decimal point moved 6 places to the right.
04

- Write in Scientific Notation

Combine the significant figures with a power of 10. Since the decimal point was moved 6 places to the right, we use 10 raised to the power of -6. Thus, the scientific notation of the number is 6.92 脳 10^{-6}.

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
In any number, significant figures are the digits that contribute meaningfully to its precision. For instance, in the number 0.00000692, the significant figures are 6, 9, and 2. These figures are important because they indicate the accuracy of the number.
Leading zeros in decimal numbers are not considered significant.
So, in 0.00000692, the leading zeros simply indicate the position of the decimal point and do not count as significant figures.
Identifying significant figures helps in accurately converting numbers into scientific notation.
decimal point
The decimal point is a critical component when converting numbers to scientific notation. It helps to place the number within a standard form between 1 and 10.
For the number 0.00000692, you need to move the decimal point to the right of the first significant figure, which is 6.
Once moved, the number becomes 6.92. Moving the decimal point helps in simplifying and standardizing the number, making it easy to express in scientific notation.
The position of the decimal point also determines the power of 10 that will be used in the conversion.
power of 10
The concept of the power of 10 is essential when converting numbers to scientific notation. It shows how many times you need to multiply or divide by 10 to get back to the original number.
In our example, after moving the decimal point, we counted how many places it moved鈥�6 places to the right.
This counting helps us determine the exponent for the power of 10. Since we moved the decimal point to the right, the exponent is negative, giving us a power of -6.
Thus, the scientific notation for 0.00000692 is 6.92 脳 10^{-6}. This notation makes it easier to handle very small (or very large) numbers in scientific calculations.

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 each expression. Assume that all variables represent nonzero real numbers. $$ \left(z^{-4} x^{3}\right)^{-1} $$

Simplify each expression. Assume that all variables represent nonzero real numbers. $$ \left(k^{2}\right)^{-3} k^{4} $$

Let \(f(x)=x^{2}-9, g(x)=2 x,\) and \(h(x)=x-3 .\) Find each of the following. $$ (f g)(2) $$

Simplify each expression. Assume that all variables represent nonzero real numbers. $$ 3^{5} \cdot 3^{-6} $$

Let \(f(x)=x^{2}-9, g(x)=2 x,\) and \(h(x)=x-3 .\) Find each of the following. $$ (f g)(2) $$
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Pure Maths

Read Explanation

Logic and Functions

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Mechanics Maths

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.