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This document discusses real numbers including the fundamental theorem of arithmetic, irrational numbers, and rational numbers and their decimal representations. It contains three sections: 1) The fundamental theorem of arithmetic states that every composite number can be uniquely expressed as a product of prime numbers. It also provides an example of using prime factorization to find the highest common factor and lowest common multiple of two numbers. 2) Irrational numbers like the square root of 2 are proven to be irrational by assuming they can be expressed as a ratio of integers and arriving at a contradiction. 3) Rational numbers with decimal representations that terminate can be expressed as a ratio of integers where the denominator is of a particular form. Other rational numbers have non-terminating
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Maths class 10th ppt.pptx
This PowerPoint presentation covers topics in Chapter 1 of Class 10 Mathematics, including real numbers, rational numbers, and their decimal representations. It discusses the fundamental theorem of arithmetic, which states that every composite number can be uniquely expressed as a product of prime numbers. It also covers finding the highest common factor and lowest common mon of two numbers using prime factorization. Finally, it proves that numbers like √2 and 3 - √5 are irrational and discusses when rational numbers have terminating or repeating decimal representations.
Real number Class 10th
In this slide you get to know the all the detail and in depth knowledge of the chapter Real Number, 1st chapter of CBSE class 10th. Here you get all the variety of questions.
You can watch the video lecture on YouTube-
https://youtu.be/T2N-NObDf8w
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This PPT is based on 10th CBSE ,NCERT Mathematics Textbook Chapter -1 Real Numbers...
I hope this will prove helpful for you....
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Euclid's division algorithm states that any positive integer a can be divided by another positive integer b with a remainder r that is smaller than b. This algorithm can be used to find the highest common factor (HCF) of two integers. The Fundamental Theorem of Arithmetic states that every composite number can be expressed as a unique product of prime numbers. These concepts are used to prove numbers like sqrt(2) and sqrt(3) are irrational and to explore when decimal expansions of rational numbers like p/q terminate or repeat.
Presentation (2).pptx
The document discusses various types of real numbers including natural numbers, whole numbers, integers, rational numbers, and irrational numbers. It provides definitions and key properties of each type of number. Examples are also given to illustrate concepts like finding the highest common factor and lowest common multiple using the Euclid division algorithm and prime factorization method. Theorems are presented to prove that certain numbers like the square root of 2 are irrational.
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This document provides an introduction to rational numbers. It defines integers, whole numbers, counting numbers, and rational numbers. Rational numbers can be expressed as the quotient of two integers, such as fractions. Some numbers, like pi, cannot be expressed as quotients of integers and are called irrational numbers. The combination of rational and irrational numbers make up the set of real numbers. The document then provides examples and theorems regarding properties of rational numbers, such as Euclid's division algorithm for finding the highest common factor of two numbers and the fundamental theorem of arithmetic regarding unique prime factorizations.
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Maths class 10th ppt.pptx
This PowerPoint presentation covers topics in Chapter 1 of Class 10 Mathematics, including real numbers, rational numbers, and their decimal representations. It discusses the fundamental theorem of arithmetic, which states that every composite number can be uniquely expressed as a product of prime numbers. It also covers finding the highest common factor and lowest common mon of two numbers using prime factorization. Finally, it proves that numbers like √2 and 3 - √5 are irrational and discusses when rational numbers have terminating or repeating decimal representations.
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In this slide you get to know the all the detail and in depth knowledge of the chapter Real Number, 1st chapter of CBSE class 10th. Here you get all the variety of questions.
You can watch the video lecture on YouTube-
https://youtu.be/T2N-NObDf8w
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This PPT is based on 10th CBSE ,NCERT Mathematics Textbook Chapter -1 Real Numbers...
I hope this will prove helpful for you....
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Euclid's division algorithm states that any positive integer a can be divided by another positive integer b with a remainder r that is smaller than b. This algorithm can be used to find the highest common factor (HCF) of two integers. The Fundamental Theorem of Arithmetic states that every composite number can be expressed as a unique product of prime numbers. These concepts are used to prove numbers like sqrt(2) and sqrt(3) are irrational and to explore when decimal expansions of rational numbers like p/q terminate or repeat.
Presentation (2).pptx
The document discusses various types of real numbers including natural numbers, whole numbers, integers, rational numbers, and irrational numbers. It provides definitions and key properties of each type of number. Examples are also given to illustrate concepts like finding the highest common factor and lowest common multiple using the Euclid division algorithm and prime factorization method. Theorems are presented to prove that certain numbers like the square root of 2 are irrational.
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This document provides an introduction to rational numbers. It defines integers, whole numbers, counting numbers, and rational numbers. Rational numbers can be expressed as the quotient of two integers, such as fractions. Some numbers, like pi, cannot be expressed as quotients of integers and are called irrational numbers. The combination of rational and irrational numbers make up the set of real numbers. The document then provides examples and theorems regarding properties of rational numbers, such as Euclid's division algorithm for finding the highest common factor of two numbers and the fundamental theorem of arithmetic regarding unique prime factorizations.
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√2 and √5 are proven to be irrational using proof by contradiction. It is assumed they can be written as fractions p/q, but this leads to contradictions as it would mean p and q have common factors, violating their definition as co-prime integers. Similarly, 3+2√5 is proven irrational by assuming it is a rational number p/q, but this again leads to a contradiction as it would mean √5 is rational.
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This document provides an overview of solving polynomial equations. It defines polynomials and their key properties like degree, coefficients, and roots. It introduces several theorems for finding roots, including the Remainder Theorem, Factor Theorem, and the idea that a polynomial of degree n has n roots when counting multiplicities. Methods discussed include factoring, long division, and the quadratic formula. The document explains it is not possible to express solutions of polynomials of degree 5 or higher using radicals.
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Key Takeaways:
Email has the best ROI of any digital tactic
It can be used at any stage of the customer journey
It is increasingly important as the cookie-less future gets closer and closerNo Cookies, No Problem - Steve Krull, Be Found Online
No Cookies, No Problem - Steve Krull, Be Found OnlineDigiMarCon - Digital Marketing, Media and Advertising Conferences & Exhibitions
In the face of the news of Google beginning to remove cookies from Chrome (30m users at the time of writing), there’s no longer time for marketers to throw their hands up and say “I didn’t know” or “They won’t go through with it”. Reality check - it has already begun - the time to take action is now. The good news is that there are solutions available and ready for adoption… but for many the race to catch up to the modern internet risks being a messy, confusing scramble to get back to "normal"How to Use AI to Write a High-Quality Article that Ranks
In the world of content creation, many AI bloggers have drifted away from their original vision, resulting in low-quality articles that search engines overlook. Don't let that happen to you! Join us to discover how to leverage AI tools effectively to craft high-quality content that not only captures your audience's attention but also ranks well on search engines.
Disclaimer: Some of the prompts mentioned here are the examples of Matt Diggity. Please use it as reference and make your own custom prompts.
Pillar-Based Marketing - Ryan Brock, DemandJump
Pillar-Based Marketing - Ryan Brock, DemandJumpDigiMarCon - Digital Marketing, Media and Advertising Conferences & Exhibitions
In this humorous and data-heavy session, join us in a joyous celebration of life honoring the long list of SEO tactics and concepts we lost this year. Remember fondly the beautiful time you shared with defunct ideas like link building, keyword cannibalization, search volume as a value indicator, and even our most cherished of friends: the funnel. Make peace with their loss as you embrace a new paradigm for organic content: Pillar-Based Marketing. Along the way, discover that the results that old SEO and all its trappings brought you weren’t really very good at all, actually.
In this respectful and life-affirming service—erm, session—join Ryan Brock (Chief Solution Officer at DemandJump and author of Pillar-Based Marketing: A Data-Driven Methodology for SEO and Content that Actually Works) and leave with:
• Clear and compelling evidence that most legacy SEO metrics and tactics have slim to no impact on SEO outcomes
• A major mindset shift that eliminates most of the metrics and tactics associated with SEO in favor of a single metric that defines and drives organic ranking success
• Practical, step-by-step methodology for choosing SEO pillar topics and publishing content quickly that ranks fastFrom Hope to Despair The Top 10 Reasons Businesses Ditch SEO Tactics.pptx
From Hope to Despair: The Top 10 Reasons Businesses Ditch SEO Tactics
Are you tired of seeing your business's online visibility plummet from hope to despair? When it comes to SEO tactics, many businesses find themselves grappling with challenges that lead them to abandon their strategies altogether. In a digital landscape that's constantly evolving, staying on top of SEO best practices is crucial to maintaining a competitive edge.
In this blog, we delve deep into the top 10 reasons why businesses ditch SEO tactics, uncovering the pain points that may resonate with you:
1. Algorithm Changes: The ever-changing algorithms can leave businesses feeling like they're chasing a moving target. Search engines like Google frequently update their algorithms to improve user experience and provide more relevant search results. However, these updates can significantly impact your website's visibility and ranking if you're not prepared.
2. Lack of Results: Investing time and resources without seeing tangible results can be disheartening. The absence of immediate results often leads businesses to lose faith in their SEO strategies. It's important to remember that SEO is a long-term game that requires patience and consistent effort.
3. Technical Challenges: From site speed issues to complex metadata implementation, technical hurdles can be daunting. Overcoming these challenges is crucial for SEO success, as technical issues can hinder your website's performance and user experience.
4. Keyword Competition: Fierce competition for top keywords can make it hard to rank effectively. Businesses often struggle to find the right balance between targeting high-traffic keywords and finding less competitive, niche keywords that can still drive significant traffic.
5. Lack of Understanding of SEO Basics: Many businesses dive into the complex world of SEO without fully grasping the fundamental principles. This lack of understanding can lead to several issues:
Keyword Awareness: Failing to recognize the importance of keyword research and targeting the right keywords in content.
On-Page Optimization: Ignorance regarding crucial on-page elements such as meta tags, headers, and content structure.
Technical SEO Best Practices: Overlooking essential aspects like site speed, mobile responsiveness, and crawlability.
Backlinks: Not understanding the value of high-quality backlinks from reputable sources.
Analytics: Failing to track and analyze data prevents businesses from optimizing their SEO efforts effectively.
6. Unrealistic Expectations and Timeframe: Entrepreneurs often fall prey to the allure of quick fixes and overnight success. Unrealistic expectations can overshadow the reality of the time and effort needed to see tangible results in the highly competitive digital landscape. SEO is a long-term strategy, and setting realistic goals is crucial for success.
#SEO #DigitalMarketing #BusinessGrowth #OnlineVisibility #SEOChallenges #BostonSEO
PickUp_conversational AI_Capex, Inc._20240610
PickUp, Improve conversions with scenario-based conversational AI.
Consumer Journey Mapping & Personalization Master Class - Sabrina Killgo
Consumer Journey Mapping & Personalization Master Class - Sabrina KillgoDigiMarCon - Digital Marketing, Media and Advertising Conferences & Exhibitions
The Secret to Engaging Modern Consumers: Journey Mapping and Personalization
In today's digital landscape, understanding the customer's journey and delivering personalized experiences are paramount. This masterclass delves into the art of consumer journey mapping, a powerful technique that visualizes the entire customer experience across touchpoints. Attendees will learn how to create detailed journey maps, identify pain points, and uncover opportunities for optimization. The presentation also explores personalization strategies that leverage data and technology to tailor content, products, and experiences to individual customers. From real-time personalization to predictive analytics, attendees will gain insights into cutting-edge approaches that drive engagement and loyalty.
Key Takeaways:
Current consumer landscape; Steps to mapping an effective consumer journey; Understanding the value of personalization; Integrating mapping and personalization for success; Brands that are getting It right!; Best Practices; Future TrendsFuture-Proof Like Beyoncé - Syncing Email and Social Media for Iconic Brand L...
Future-Proof Like Beyoncé - Syncing Email and Social Media for Iconic Brand L...DigiMarCon - Digital Marketing, Media and Advertising Conferences & Exhibitions
In this dynamic session titled "Future-Proof Like Beyoncé: Syncing Email and Social Media for Iconic Brand Longevity," Carlos Gil, U.S. Brand Evangelist for GetResponse, unveils how to safeguard and elevate your digital marketing strategy. Explore how integrating email marketing with social media can not only increase your brand's reach but also secure its future in the ever-changing digital landscape. Carlos will share invaluable insights on developing a robust email list, leveraging data integration for targeted campaigns, and implementing AI tools to enhance cross-platform engagement. Attendees will learn how to maintain a consistent brand voice across all channels and adapt to platform changes proactively. This session is essential for marketers aiming to diversify their online presence and minimize dependence on any single platform. Join Carlos to discover how to turn social media followers into loyal email subscribers and ultimately, drive sustainable growth and revenue for your brand. By harnessing the best practices and innovative strategies discussed, you will be equipped to navigate the challenges of the digital age, ensuring your brand remains relevant and resonant with your audience, no matter the platform. Don’t miss this opportunity to transform your approach and achieve iconic brand longevity akin to Beyoncé's enduring influence in the entertainment industry.
Key Takeaways:
Integration of Email and Social Media: Understanding how to seamlessly integrate email marketing with social media efforts to expand reach and reinforce brand presence. Building a Robust Email List: Strategies for developing a strong email list that provides a direct line of communication to your audience, independent of social media algorithms. Data Integration for Targeted Campaigns: Leveraging combined data from email and social media to create personalized, targeted marketing campaigns that resonate with the audience. Utilization of AI Tools: Implementing AI and automation tools to enhance efficiency and effectiveness across marketing channels. Consistent Brand Voice Across Platforms: Maintaining a unified brand voice and message across all digital platforms to strengthen brand identity and user trust. Proactive Adaptation to Platform Changes: Staying ahead of social media platform changes and algorithm updates to keep engagement high and interactions meaningful. Conversion of Social Followers to Email Subscribers: Techniques to encourage social media followers to subscribe to email, ensuring a direct and consistent connection. Sustainable Growth and Minimized Platform Dependence: Strategies to diversify digital presence and reduce reliance on any single social media platform, thereby mitigating risks associated with platform volatility.How American Bath Group Leveraged Kontent
How American Bath Group Leveraged KontentDigiMarCon - Digital Marketing, Media and Advertising Conferences & Exhibitions
We will explore the transformative journey of American Bath Group as they transitioned from a traditional monolithic CMS to a dynamic, composable martech framework using Kontent.ai. Discover the strategic decisions, challenges, and key benefits realized through adopting a headless CMS approach. Learn how composable business models empower marketers with flexibility, speed, and integration capabilities, ultimately enhancing digital experiences and operational efficiency. This session is essential for marketers looking to understand the practical impacts and advantages of composable technology in today's digital landscape. Join us to gain valuable insights and actionable takeaways from a real-world implementation that redefines the boundaries of marketing technology.Pillar-Based Marketing Master Class - Ryan Brock
Pillar-Based Marketing Master Class - Ryan BrockDigiMarCon - Digital Marketing, Media and Advertising Conferences & Exhibitions
In this humorous and data-heavy Master Class, join us in a joyous celebration of life honoring the long list of SEO tactics and concepts we lost this year. Remember fondly the beautiful time you shared with defunct ideas like link building, keyword cannibalization, search volume as a value indicator, and even our most cherished of friends: the funnel. Make peace with their loss as you embrace a new paradigm for organic content: Pillar-Based Marketing. Along the way, discover that the results that old SEO and all its trappings brought you weren’t really very good at all, actually.
In this respectful and life-affirming service—erm, session—join Ryan Brock (Chief Solution Officer at DemandJump and author of Pillar-Based Marketing: A Data-Driven Methodology for SEO and Content that Actually Works) and leave with:
• Clear and compelling evidence that most legacy SEO metrics and tactics have slim to no impact on SEO outcomes
• A major mindset shift that eliminates most of the metrics and tactics associated with SEO in favor of a single metric that defines and drives organic ranking success
• Practical, step-by-step methodology for choosing SEO pillar topics and publishing content quickly that ranks fastHow To Navigate AI - The Future is Yours to Define - Tim Hayden
How To Navigate AI - The Future is Yours to Define - Tim HaydenDigiMarCon - Digital Marketing, Media and Advertising Conferences & Exhibitions
As 2023 proved, the next few years may be shaped by market volatility and artificial intelligence services such as OpenAI's ChatGPT and Perplexity.ai. Your brand will increasingly compete for attention with Google, Apple, OpenAI, and Amazon, and customers will expect a hyper-relevant and individualized experience from every business at any moment. New state-legislated data privacy laws and several FTC rules may challenge marketers to deliver contextually relevant customer experiences, much less reach unknown prospective buyers. Are you ready?Let's discuss the critical need for data governance and applied AI for your business rather than relying on public AI models. As AI permeates society and all industries, learn how to be future-ready, compliant, and confidentlyscaling growth.
Key Takeaways:
Primary Learning Objective
1: Grasp when artificial general intelligence (""AGI"") will arrive, and how your brand can navigate the consequences. Primary Learning Objective
2: Gain an accurate analysis of the continuously developing customer journey and business intelligence. Primary Learning Objective
3: Grow revenue at lower costs with more efficient marketing and business operations.Gokila digital marketing| consultant| Coimbatore
Myself Gokila digital marketing consultant located in Coimbatore other various types of digital marketing services such as SEM
SEO SMO SMM CAMPAIGNS content writing web design for all your business needs with affordable cost
Digital Marketing Services | Techvolt Software :
Digital Marketing is a latest method of Marketing techniques widely used across the Globe. Digital Marketing is an online marketing technique and methods used for all products and services through Search Engine and Social media advertisements. Previously the marketing techniques were used without using the internet via direct and indirect marketing strategies such as advertising through Telemarketing,Newspapers,Televisions,Posters etc.
List of Services offered in Digital Marketing |Techvolt Software :
Techvolt Software offers best Digital Marketing services for promoting your products and services through online platform on the below methods of Digital marketing
1. Search Engine Optimization (SEO)
2. Search Engine Marketing (SEM)
3. Social Media Optimization (SMO)
4. Social Media Marketing (SMM)
5. Campaigns
Importance | Need of Digital Marketing (Online Promotions) :
1. Quick Promotions through Online
2. Generation of More leads and Business Enquiries via Search Engine and Social Media Platform
3. Latest Technology development vs Business promotions
4. Creation of Social Branding
5. Promotion with less investment
Benefits Digital Marketing Services at Techvolt software :
1. Services offered with Affordable cost
2. Free Content writing
3. Free Dynamic Website design*
4. Best combo offers on website Hosting,design along with digital marketing services
5. Assured Lead Generation through Search Engine and Social Media
6. Online Maintenance Support
Free Website + Digital Marketing Services
Techvolt Software offers Free website design for all customer and clients who is availing the digital marketing services for a minimum period of 6 months.
With Regards
Gokila digital marketer
Coimbatore
Global Growth Starts With Translation - How To Unlock Global Markets - Tim Kirby
Global Growth Starts With Translation - How To Unlock Global Markets - Tim KirbyDigiMarCon - Digital Marketing, Media and Advertising Conferences & Exhibitions
Did you know that while 50% of content on the internet is in English, English only makes up 26% of the world’s spoken language? And yet 87% of customers won’t buy from an English only website.
Uncover the immense potential of communicating with customers in their own language and learn how translation holds the key to unlocking global growth. Join Smartling CEO, Bryan Murphy, as he reveals how translation software can streamline the translation process and seamlessly integrate into your martech stack for optimal efficiency. And that's not all – he’ll also share some inspiring success stories and practical tips that will turbocharge your multilingual marketing efforts!
Key takeaways:
1. The growth potential of reaching customers in their native language
2. Tips to streamline translation with software and integrations to your tech stack
3. Success stories from companies that have increased lead generation, doubled revenue, and more with translationRecently uploaded (20)
AI Driven Emotional Recognition in Digital Ads - Tarun Gupta
AI Driven Emotional Recognition in Digital Ads - Tarun Gupta
Luxury Hanloom Saree Brand ,Capstone Project_Kiran Bansal.pdf
Luxury Hanloom Saree Brand ,Capstone Project_Kiran Bansal.pdf
Digital Marketing Trends - Experts Insights on How to Gain a Competitive Edge...
Digital Marketing Trends - Experts Insights on How to Gain a Competitive Edge...
Marketing in the Age of AI - Shifting CX from Monologue to Dialogue - Susan W...
Marketing in the Age of AI - Shifting CX from Monologue to Dialogue - Susan W...
Mastering SEO for Google in the AI Era - Dennis Yu
Mastering SEO for Google in the AI Era - Dennis Yu
No Cookies, No Problem - Steve Krull, Be Found Online
No Cookies, No Problem - Steve Krull, Be Found Online
How to Use AI to Write a High-Quality Article that Ranks
How to Use AI to Write a High-Quality Article that Ranks
From Hope to Despair The Top 10 Reasons Businesses Ditch SEO Tactics.pptx
From Hope to Despair The Top 10 Reasons Businesses Ditch SEO Tactics.pptx
Consumer Journey Mapping & Personalization Master Class - Sabrina Killgo
Consumer Journey Mapping & Personalization Master Class - Sabrina Killgo
Future-Proof Like Beyoncé - Syncing Email and Social Media for Iconic Brand L...
Future-Proof Like Beyoncé - Syncing Email and Social Media for Iconic Brand L...
How To Navigate AI - The Future is Yours to Define - Tim Hayden
How To Navigate AI - The Future is Yours to Define - Tim Hayden
Global Growth Starts With Translation - How To Unlock Global Markets - Tim Kirby
Global Growth Starts With Translation - How To Unlock Global Markets - Tim Kirby
Presentation.pptx
- 1. REAL NUMBERS 1.The fundamental theorem of Arithmetic. 2. Revisiting irrational numbers. 3.Revisiting rational numbers and their decimal representation.
- 2. THE FUNDAMENTAL THEOREM OF ARITHMETIC Every composite number can be expressed (factorised) as a product of primes, and this factorization is unique. The method of finding the HCF and LCM of two positive numbers by the prime factorization method. Example: Find HCF and LCM of 108 and 150 108 =2² X 3³ and 150 =2 X 3 X 5² HCF(108,150) =2 X3 = Product of SMALLEST power of each common prime factor in the numbers. LCM(108,150)= 2² X 3³ X5² = Product of GREATEST power of each common prime factor in the numbers. Notice that HCF(108,150) X LCM(108,150)= 108 X150
- 3. REVISITING IRRATIONAL NUMBERS In this section, we will prove that numbers of the form √p are irrational where p is a prime. Example: Prove √2 is irrational. Proof: Assume √2 is rational. Then √2 =a/b ,where a and b are co- prime and b≠ 0. Squaring both sides, we get 2b² = a² , i.e. 2 divides a²,implies 2 divides a. Let a=2c.Then , substituting for a, we get 2b²=4c² i.e.b² = 2c² This means that 2 divides b²,and so divides b. Therefore, a and b have at least 2 as a common factor. This contradicts the fact a and b have no common factors other than 1. So, we conclude that √2 is irrational. Similarly, we can prove that √3 ,√5 etc are irrational.
- 4. Proving Irrational Numbers Example: Show that 3 − √5 is irrational. Proof: Assume 3 − √5 is rational. Then 3 − √5=a/b, where and b are co-prime,b≠0. Rearranging the equation, we get √5=3 − (a/b) = (3b − a)/b Since a and b are integers (3b − a)/b is rational, and so , √5 is rational. This contradicts the fact that √5 is irrational. Therefore, our assumption is wrong
- 5. REVISITING RATIONAL NUMBERS AND THEIIR DECIMAL REPRESENTATION - I Theorem 1: Let x be a rational number whose decimal expansion terminates. Then ,x can be expressed in the form p/q, where p and q are coprime ,and the prime-factorisation of q is in the form 2 n5m where n and m are non-negative integers. Example : 0.107 = 107/1000= 107/(2³ x 5³ ) Example: 7.28 = 728/100 = 728 / 10²
- 6. REVISITING RATIONAL NUMBERS AND THEIR DECIMAL REPRESENTATION - II Theorem 2 : Let x = p/q be a rational number such that prime factorisation of q is of the form 2 n5m where n and m are non-negative integers. Then x has a decimal representation that terminates. Example: 3/8 = 3/2³ = 0.375 Example: 13/250=13/ 2 x 5³ = 0.052
- 7. REVISITING RATIONAL NUMBERS AND THEIR DECIMAL REPRESENTATION - III Theorem 3 : Let x=p/q ,where p and q are coprimes be a rational number such that prime factorisation of q is not of the form 2 n5m ,where n and m are non-negative integers. Then ,x has a decimal expansion which is nonterminating repeating.