/*! 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 31 Express answers in standard nota... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Problem 31

Express answers in standard notation. $$ \frac{12 \times 10^{4}}{2 \times 10^{6}} $$

Short Answer

Expert verified
0.06

Step by step solution

01

Divide the Coefficients

First, divide the coefficients of the numbers. Divide 12 by 2: o 12 梅 2 = 6
02

Subtract the Exponents

Next, subtract the exponent of the denominator from the exponent of the numerator. 4 - 6 = -2
03

Combine the Results

Now, combine the results from Step 1 and Step 2. The answer will be the coefficient from Step 1 multiplied by 10 raised to the power obtained in Step 2. o 6 脳 10^{-2}
04

Express in Standard Notation

Finally, express the answer in standard notation. o 6 脳 10^{-2} = 0.06

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.

Dividing Coefficients
When working with scientific notation, the first step is to handle the coefficients. Coefficients are the numbers that are multiplied by 10 raised to a power. In the given exercise, the coefficients are 12 and 2. Dividing these coefficients is straightforward: simply divide the numerator by the denominator. So, calculate \(\frac{12}{2} = 6\). This step simplifies the numerical part of the fraction before you deal with the exponents.
Subtracting Exponents
After dividing the coefficients, the next step is to subtract the exponents. Exponents in scientific notation represent powers of 10. In the provided exercise, the exponents are 4 (for the numerator) and 6 (for the denominator). To handle this, subtract the exponent in the denominator from the exponent in the numerator: \(4 - 6 = -2\). This result will be the new exponent for 10 in the simplified expression.
Standard Notation
The final step is to combine the simplified coefficient and the new exponent to express the result in standard notation. From earlier steps, we have the simplified coefficient as 6, and the new exponent as -2. Combine these to get \(6 \times 10^{-2}\). Finally, convert this back into standard notation: \(6 \times 10^{-2} = 0.06\). Standard notation is simply a way of writing numbers without exponents and in this case, it shows us that the original complex expression simplifies to an easy-to-read decimal form, which is 0.06.

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

Write using only positive exponents and then evaluate. Assume that all variables represent nonzero real numbers. $$ \left(\frac{1}{4 x}\right)^{-2} $$

Find each product. $$ [(2 a+b)-3]^{2} $$

Perform the indicated operations. $$ 5 k-(5 k-[2 k-(4 k-8 k)])+11 k-(9 k-12 k) $$

Find each product. $$ [(5 x+1)+6 y]^{2} $$

Write using only positive exponents and then evaluate. Assume that all variables represent nonzero real numbers. $$ \left(\frac{1}{5 x}\right)^{-3} $$
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Probability and Statistics

Read Explanation

Discrete Mathematics

Read Explanation

Calculus

Read Explanation

Pure Maths

Read Explanation

Logic and Functions

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.