/*! 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 48 Convert each number into standar... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 7: Problem 48

Convert each number into standard notation. $$78,951 \times 10^{-5}$$

Short Answer

Expert verified
0.78951

Step by step solution

01

Understanding Scientific Notation

The given number is in scientific notation: \( 78,951 \times 10^{-5} \). Scientific notation is a way of expressing numbers that are too big or too small to be conveniently written in decimal form.
02

Identify the Power of Ten

In the expression \( 78,951 \times 10^{-5} \), the power of ten is \( 10^{-5} \). This means the decimal point will move 5 places to the left.
03

Move the Decimal Point

Starting with the number 78,951, move the decimal point 5 places to the left. Each move left decreases the number by a factor of 10. This turns 78,951 into 0.78951.

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.

Standard Notation
Standard notation is a way to write numbers without using exponents or scientific notation. It鈥檚 the most common way of representing numbers. For example, the number 7,895 is in standard notation. When you convert a number from scientific notation to standard notation, you are simply writing it out in full form without any powers of ten (e.g., transforming\(78,951 \times 10^{-5}\)to 0.78951). This often involves moving the decimal point to expand the number into a more readable form.
Power of Ten
The power of ten is a very important concept in scientific notation. In the format \(a \times 10^n\), the term 'power of ten' refers to the \(10^n\)part. Here, 'n' is the exponent and determines how many places to move the decimal point. A positive power of ten (e.g.,\(10^3\))means you move the decimal point to the right. A negative power of ten (e.g.,\(10^{-3}\))means you move the decimal point to the left.
In the original exercise, the number\(78,951 \times 10^{-5}\) has\(10^{-5}\) as the power of ten, which moves the decimal point 5 places to the left, resulting in 0.78951.
Decimal Point
The decimal point is a dot (.) used to separate the whole number part from the fractional part of a number. It plays a crucial role when converting between scientific and standard notation. For example, in the number 78,951, the decimal point is implicitly at the end (78,951.).
When you see a power of ten with a negative exponent, it tells you to move the decimal point to the left. Starting from 78,951, moving the decimal point 5 places to the left will make it 0.78951. This is how you convert\(78,951 \times 10^{-5}\)into standard notation: by adjusting the position of the decimal point according to the power of ten.

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

Do your computations using scientific notation. The thickness of a typical cell wall might be 153 A. Write this number in scientific notation.

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. $$(2 a-5)^{2}$$

Estimate the answer without actually carrying out the computation and make the most appropriate choice. If you divide \(9.28 \times 10^{7}\) by \(6.86 \times 10^{4},\) the result is closest to (a) 10 (b) 100 (c) 1000 (d) 0.1 (e) 0.01

Convert each number into standard notation. $$4.29 \times 10^{-7}$$

Estimate the answer without actually carrying out the computation and make the most appropriate choice. If you multiply \(1.93 \times 10^{5}\) by \(5.12 \times 10^{-3},\) the result is closest to (a) 10 (b) 1000 (c) \(10,000\) (d) 0.01 (e) 0.001
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Statistics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Probability and Statistics

Read Explanation

Applied Mathematics

Read Explanation

Pure Maths

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.