/*! 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 33 Write each number without expone... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 33

Write each number without exponents. $$ 7.8 \times 10^{-4} $$

Short Answer

Expert verified
0.00078

Step by step solution

01

Understand the Exponent

The exponent ief10^{-4}ie indicates that the decimal point should move 4 places to the left.
02

Move the Decimal Point

Start with the number 7.8. Moving the decimal point 4 places to the left means filling in 3 zeros to the left of 7.
03

Write the Final Number

The final number after moving the decimal point is 0.00078.

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.

Exponents
Exponents play a crucial role in scientific notation. They show how many times a number should be multiplied by itself. For example, in the expression \(10^{-4}\), the exponent -4 indicates that the number 10 should be used as a fraction where it's repeatedly divided by itself.
Here are the steps for working with exponents in scientific notation:
  • Identify the base, which is often 10 in scientific notation.
  • Look at the exponent to determine the direction and number of movements for the decimal point.
  • A negative exponent tells you to move the decimal point to the left.
  • A positive exponent instructs you to move the decimal point to the right.
Understanding exponents helps in transforming numbers effectively between their expanded form and scientific notation.
Decimal Point
A decimal point is a symbol used to separate the whole number part from the fractional part of a number. Moving the decimal point correctly is essential when working with scientific notation. Here's how:
  • Start with the given number.
  • Observe the exponent to know how many places to move the decimal point.
  • For \(10^{-4}\), you move the decimal point 4 places to the left.
In the given exercise, the starting number is 7.8. Moving the decimal point 4 places to the left involves adding three zeros before 7. The result is 0.00078. Remember, moving the decimal point adjusts the numerical value but not the number itself.
Standard Form
Standard form, also known as scientific notation, is a way to express very large or very small numbers concisely. The format is \(a \times 10^{n}\), where 'a' is a number greater than or equal to 1 but less than 10, and 'n' is an integer exponent.
This form is beneficial for simplifying calculations and comparisons of significantly different sized numbers. Here鈥檚 how to convert to and from standard form:
  • Identify 'a' by moving the decimal point to create a number between 1 and 10.
  • Count the number of places the decimal point was moved to establish the exponent 'n'.
  • If you moved the decimal to the left, 'n' is positive; if to the right, 'n' is negative.
For example, 70000 in standard form is \(7 \times 10^{4}\), and 0.00078 converted is \(7.8 \times 10^{-4}\). This compact form makes complex numbers easier to handle and understand.

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

Perform each division. $$ \frac{-4 x+3 x^{3}+2}{x-1} $$

Perform each division. $$ \frac{x^{4}-4 x^{3}+5 x^{2}-3 x+2}{x^{2}+3} $$

List all positive integer factors of each number. $$ 36 $$

Evaluate each expression for \(x=3\) $$ -4 x^{3}+2 x^{2}-9 x-2 $$

Find each product. \((3 r+5)(2 r+1)\)
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Decision Maths

Read Explanation

Geometry

Read Explanation

Pure Maths

Read Explanation

Logic and Functions

Read Explanation

Mechanics 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.