/*! 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 39 Convert each number into standar... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 7: Problem 39

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

Short Answer

Expert verified
42,900,000

Step by step solution

01

Understand Scientific Notation

Scientific notation is a way to express very large or very small numbers. It is written as the product of a number (usually between 1 and 10) and a power of 10. In this case, the given number is written as \(4.29 \times 10^{7}\).
02

Identify the Components

Here, the decimal number is 4.29, and the exponent is 7. The exponent indicates how many places to move the decimal point to the right for a positive number.
03

Move the Decimal Point

Move the decimal point 7 places to the right: 4.29 becomes 42900000 when the decimal point is moved 7 places to the right.
04

Write the Number in Standard Notation

After moving the decimal point, the number in standard notation is 42,900,000.

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.

numbers in scientific notation
Scientific notation is a method used to simplify very large or very small numbers, making them easier to work with. It involves expressing the number as the product of a coefficient (a number between 1 and 10) and a power of 10. For example, the number \(4.29 \times 10^{7}\) indicates that 4.29 is multiplied by 10 raised to the power of 7. This notation is particularly useful in fields like science and engineering where such numbers are common. It simplifies calculations and allows for easier comparison of magnitudes.
moving decimal points
Converting from scientific notation to standard notation involves moving the decimal point based on the exponent of 10. In the example \(4.29 \times 10^{7}\), the exponent is 7. This tells us to move the decimal point 7 places to the right.
If the exponent were negative, we would move the decimal point to the left instead. Here's how it works:
  • If the exponent is positive, move the decimal point to the right.
  • If the exponent is negative, move the decimal point to the left.
When moving the decimal point, if there are not enough digits, zeros are added to fill in the gaps.
standard notation
Standard notation is the regular way of writing numbers without exponents. For example, converting \(4.29 \times 10^{7}\) into standard notation involves moving the decimal point 7 places to the right, resulting in 42,900,000.
Standard notation is straightforward and easy to read, but it can become cumbersome for very large or very small numbers. Hence, scientific notation is used to simplify and manage these numbers more efficiently.
Understanding how to convert between scientific and standard notation is crucial for clarity and simplicity in mathematical and 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

A long pole is standing slightly offshore. If one quarter of the pole is in the sand, \(8 \mathrm{ft}\) is in the water, and two thirds of the pole is in the air, how long is the pole?

If an 8 by 10 rectangle is cut out of a square of side \(x,\) express the remaining area in terms of \(x .\) (We must assume that \(x>10 .\) Why?)

Estimate the answer without actually carrying out the computation and make the most appropriate choice. If you divide 2350 by \(48,600\), the result is closest to (a) 0.05 (b) 0.5 (c) 5 (d) 50 (e) 500

Convert each number into standard notation. $$0.026 \times 10^{-3}$$

What can you say about the sign of the exponent of 10 of a number written in scientific notation if the number is bigger than \(1 ?\) If the number is smaller than \(1 ?\) Why?
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Discrete Mathematics

Read Explanation

Decision Maths

Read Explanation

Pure Maths

Read Explanation

Geometry

Read Explanation

Applied Mathematics

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.