/*! 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 24 Convert each number into scienti... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 7: Problem 24

Convert each number into scientific notation. $$37$$

Short Answer

Expert verified
3.7 \times 10^1

Step by step solution

01

Identify the number

Recognize the given number. In this case, the number to be converted is 37.
02

Move the Decimal Point

Move the decimal point so that there is only one non-zero digit to the left of the decimal. For 37, move the decimal one place to the left, yielding 3.7.
03

Count the Decimal Places

Count the number of places the decimal point was moved. Here, it was moved 1 place to the left.
04

Express in Scientific Notation

Combine the number and the power of 10. Since we moved the decimal 1 place to the left, the exponent will be positive. Thus, 37 can be written as \(3.7 \times 10^1\).

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.

Understanding the Decimal Point
When dealing with numbers in scientific notation, the decimal point plays a critical role. The decimal point separates the integer part of a number from the fractional part. For instance, in the number 3.7, '3' is the integer part and '.7' is the fractional part.
To convert a number to scientific notation, you need to place the decimal point such that there is only one non-zero digit to its left.
This keeps the number between 1 and 10. In our example, the number 37 becomes 3.7 when we move the decimal point one place to the left.
What is a Positive Exponent?
In scientific notation, exponents denote the number of times you multiply or divide by 10. A positive exponent signifies that the decimal point was moved to the left.
This often indicates a larger number because you are counting how many times to multiply by 10 to return to the original number.
For our example, moving the decimal point to the left by one place from 37 to 3.7, we get an exponent of +1. Thus, 37 becomes \(3.7 \times 10^1\).
This process helps simplify very large or very small numbers.
Numbers Conversion Explained
The process of converting numbers into scientific notation involves a few simple steps.
First, identify the number you want to convert. Next, move the decimal point so that there鈥檚 only one non-zero digit to its left.
Count the number of places the decimal point was moved. Finally, combine the resulting number with a power of 10.
The power of 10 is determined by the number of places the decimal point was originally moved.
  • If moved left, the exponent is positive.
  • If moved right, it is negative.
For the number 37, since we moved the decimal one place to the left, the result is \(3.7 \times 10^1\).
This makes it easier to grasp and work with large numbers.

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

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. $$(3 y-4)^{2}$$

Solve for x. $$-2<3 x+4 \leq 16$$

If a square of side \(x\) is cut out of a rectangle whose dimensions are 8 by 10 express the remaining area in terms of \(x\).

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

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. $$(2 a+5)(2 a-5)$$
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Decision Maths

Read Explanation

Statistics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Geometry

Read Explanation

Discrete 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.