/*! 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 25 Write each number without expone... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 25

Write each number without exponents. $$ 7.5 \times 10^{5} $$

Short Answer

Expert verified
750000

Step by step solution

01

Understand the Exponent

The given number is written in scientific notation: \(7.5 \times 10^{5}\). The exponent 5 indicates that the decimal point should move 5 places to the right.
02

Move the Decimal Point

Starting with 7.5, move the decimal point 5 places to the right. This means adding five zeros after the 7 and shifting the decimal point past these zeros.
03

Write the Result

After moving the decimal point 5 places, the number becomes 750000. Thus, \(7.5 \times 10^{5}\) without exponents is written as 750000.

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 are a way to express repeated multiplication of the same number. For example, in the expression \(10^5\), the number 10 is the base, and 5 is the exponent. This tells us to multiply 10 by itself 5 times:
  • \(10^1 = 10\)
  • \(10^2 = 10 \times 10 = 100\)
  • \(10^3 = 10 \times 10 \times 10 = 1000\)
  • And so on...
In scientific notation, exponents are used to show how many times the base (usually 10) should be multiplied or divided. This is especially useful for working with very large or very small numbers.
Decimal Point
A decimal point is a dot used to separate the whole number part from the fractional part of a number. For example, in the number 7.5, 7 is the whole number part, and 5 is the fractional part.
When working with exponents in scientific notation, you often need to move the decimal point to convert the number into its standard form.
In the example given (\(7.5 \times 10^5\)), the decimal point in 7.5 moves 5 places to the right to form the number 750000. This shifts the position of the decimal point by adding zeros until you reach the correct place.
Standard Form
Standard form is a way of writing numbers without using exponents. It shows the actual value of the number. To convert a number from scientific notation to standard form, you need to move the decimal point according to the exponent.
In our example, \(7.5 \times 10^5\) converts to 750000 in standard form. Here is how it works:
  • Recognize the exponent 5 means moving the decimal point 5 places to the right.
  • Move the decimal point 5 places to the right, adding zeros as needed.
  • The number becomes 750000.
Using standard form simplifies numbers and makes them easier to read and understand, especially when dealing with very large or very small quantities.

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

The special product $$ (x+y)(x-y)=x^{2}-y^{2} $$ $$ \text { can be used to perform some multiplication problems. Here are two examples.} $$ $$ \begin{aligned} 51 \times 49 &=(50+1)(50-1) \\ &=50^{2}-1^{2} \\ &=2500-1^{2} \\ &=2499 \end{aligned} \quad | \begin{aligned} 102 \times 98 &=(100+2)(100-2) \\ &=100^{2}-2^{2} \\ &=10,000-4 \\ &=9996 \end{aligned} $$ Once these patterns are recognized, multiplications of this type can be done mentally. Use this method to calculate each product mentally. $$ 101 \times 99 $$

Find each product. \(-3 k\left(8 k^{2}-12 k+2\right)\)

Simplify by writing each expression wth positive exponents. Assume that all variables represent nonzero real numbers. $$ \frac{\left(3 p^{-2} q^{3}\right)^{2}\left(5 p^{-1} q^{-4}\right)^{-1}}{\left(p^{2} q^{-2}\right)^{-3}} $$

Find each product. \(-5 r(r+1)^{3}\)

Perform each indicated operation. Find the difference between the sum of \(5 x^{2}+2 x-3\) and \(x^{2}-8 x+2\) and the sum of \(7 x^{2}-3 x+6\) and \(-x^{2}+4 x-6\)
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Discrete Mathematics

Read Explanation

Geometry

Read Explanation

Decision Maths

Read Explanation

Mechanics Maths

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.