Short Tricks to Find Unit Digit of an Expression (1)

Duration: 15 min

This video lesson is available to enrolled students.

Return to /learn/CTET-PAPER-1/mathematics/hcflcm-factors-divisibility-hcflcm/remainders-units-digits-t80b4p/asset-short-tricks-to-find-unit-digit-of-an-expression-1 after enrolling

Inside: a video lesson and guided study material.

Module outline

  1. Child Development and Pedagogy / बाल विकास एवं शिक्षाशास्त्र: Concept of Development / विकास की अवधारणा, Psychological Theories of Development / विकास के मनोवैज्ञानिक सिद्धांत, Individual Differences, Personality and Gender / व्यक्तिगत भिन्नताएँ, व्यक्तित्व एवं जेंडर, Intelligence and Creativity / बुद्धि एवं सृजनात्मकता, Learning and Its Theories / अधिगम एवं इसके सिद्धांत, How Children Think and Learn / बालक कैसे सोचते एवं सीखते हैं, Emotion, Motivation, Mental Health and Guidance / संवेग, अभिप्रेरणा, मानसिक स्वास्थ्य एवं निर्देशन, Inclusive Education / समावेशी शिक्षा, Teaching-Learning Process / शिक्षण-अधिगम प्रक्रिया, Teaching Methods and Strategies / शिक्षण विधियाँ एवं रणनीतियाँ, Assessment and Evaluation / आकलन एवं मूल्यांकन, Curriculum and School Activities / पाठ्यचर्या और विद्यालयी गतिविधियाँ, Lesson Planning and Teaching Skills / पाठ योजना और शिक्षण कौशल, Teaching Resources and Educational Technology / शिक्षण संसाधन और शैक्षिक प्रौद्योगिकी, Educational Thinkers, Aims and National Policies / शैक्षिक विचारक, उद्देश्य एवं राष्ट्रीय नीतियाँ, Classroom Management and Communication / कक्षा प्रबंधन और सम्प्रेषण, Teacher Identity and Professional Development / शिक्षक पहचान और व्यावसायिक विकास, Social Science Pedagogy / सामाजिक विज्ञान शिक्षणशास्त्र, Social and Political Life / सामाजिक एवं राजनीतिक जीवन, Science Pedagogy / विज्ञान शिक्षण शास्त्र, Life Skills, Values, Peace and Environmental Education / जीवन कौशल, मूल्य, शांति एवं पर्यावरण शिक्षा, Constitution, Commissions, Acts and Schemes in Education / संविधान, आयोग, अधिनियम एवं योजनाएँ
  2. Mathematics / गणित: Number System & Place Value / संख्या पद्धति एवं स्थानीय मान, Basic Operations, Simplification & Patterns / मूलभूत संक्रियाएँ, सरलीकरण एवं पैटर्न, Factors, Divisibility, HCF & LCM / गुणनखंड, विभाज्यता, म.स.प. एवं ल.स.प., Fractions & Decimals / भिन्न एवं दशमलव, Squares, Cubes, Exponents & Surds / वर्ग, घन, घातांक एवं करणी, Measurement: Length, Mass, Capacity, Time & Money / मापन: लंबाई, भार, धारिता, समय एवं मुद्रा, Algebra / बीजगणित, Ratio, Proportion, Average & Ages / अनुपात, समानुपात, औसत एवं आयु, Percentage, Profit–Loss & Interest / प्रतिशत, लाभ-हानि एवं ब्याज, Time & Work and Speed–Distance / समय-कार्य एवं चाल-दूरी, Lines, Angles, Shapes & Coordinates / रेखाएँ, कोण, आकृतियाँ एवं निर्देशांक, Triangles, Quadrilaterals, Circles & Trigonometry / त्रिभुज, चतुर्भुज, वृत्त एवं त्रिकोणमिति, Mensuration: Perimeter, Area & Volume / क्षेत्रमिति: परिमाप, क्षेत्रफल एवं आयतन, Data Handling, Statistics & Probability / आँकड़ा प्रबंधन, सांख्यिकी एवं प्रायिकता, Mathematics Pedagogy / गणित शिक्षणशास्त्र, Alphabet & Number Test / वर्णमाला एवं संख्या परीक्षण, Non-Verbal Reasoning / अशाब्दिक तर्क, Dice & Cubes / पासा एवं घन, Mathematical Operations & Arithmetical Reasoning / गणितीय संक्रियाएँ एवं अंकगणितीय तर्क, Ranking, Seating Arrangement & Puzzles / क्रम, बैठक व्यवस्था एवं पहेली, Calendar & Clock / कैलेंडर एवं घड़ी, Venn Diagrams & Logical Deduction / वेन आरेख एवं तार्किक निगमन
  3. Environmental Studies / पर्यावरण अध्ययन: Family, Friends and Community / परिवार, मित्र और समुदाय, Plants / पौधे, Animals / जंतु, Farming and Animal Husbandry / खेती और पशुपालन, Food and Nutrition / भोजन और पोषण, Body and Health / शरीर और स्वास्थ्य, Water / जल, Shelter / आवास, Travel, Transport and Communication / यात्रा, परिवहन और संचार, Maps, Directions and India / मानचित्र, दिशाएँ और भारत, Things We Make and Do / हम क्या बनाते और करते हैं, Earth, Sky and Disasters / पृथ्वी, आकाश और आपदाएँ, Environment, Ecology and Wildlife / पर्यावरण, पारिस्थितिकी और वन्यजीव, Natural Resources, Pollution and Climate Change / प्राकृतिक संसाधन, प्रदूषण और जलवायु परिवर्तन, Pedagogy of Environmental Studies / पर्यावरण अध्ययन का शिक्षणशास्त्र, Physical Geography / भौतिक भूगोल, Resources and Development / संसाधन एवं विकास, Force, Pressure, Work and Energy / बल, दाब, कार्य एवं ऊर्जा, Environment and Ecology / पर्यावरण एवं पारिस्थितिकी, Science & Technology / विज्ञान एवं प्रौद्योगिकी, Heat and Sound / ऊष्मा एवं ध्वनि, Light / प्रकाश, Universe and Natural Phenomena / ब्रह्मांड एवं प्राकृतिक परिघटनाएँ, Chemical Reactions, Acids, Bases and Salts / रासायनिक अभिक्रियाएँ, अम्ल, क्षार एवं लवण, Natural Vegetation, Wildlife and World Regions / प्राकृतिक वनस्पति, वन्य जीवन एवं विश्व के प्रदेश, Environment & Climate Affairs / पर्यावरण एवं जलवायु समसामयिकी
  4. Language I/II — हिंदी / Hindi: भाषा, लिपि और वर्ण-विचार, संधि, शब्द-स्रोत और शब्द-रचना, समास, शब्द-भेद: विकारी और अविकारी, लिंग, वचन, कारक, काल और वाच्य, वाक्य-विचार और शुद्ध लेखन, शब्द-भंडार, रस, छंद, अलंकार और शब्द-शक्ति, हिंदी साहित्य, अपठित बोध, हिंदी शिक्षणशास्त्र
  5. Language I/II — English: Sounds, Spelling and Word Formation, Parts of Speech, Nouns and Pronouns, Articles, Determiners and Adjectives, Verbs and Modals, Tenses and Subject–Verb Agreement, Adverbs, Prepositions and Conjunctions, Sentence Structure, Voice and Narration, Vocabulary, Sentence Correction and Writing Skills, Poetry and English Literature, Reading Comprehension, Pedagogy of English Language
  6. Language I/II — संस्कृत / Sanskrit: वर्णविचारः एवं संज्ञाप्रकरणम्, सन्धिप्रकरणम्, शब्दरूपाणि, धातुरूपाणि, कारकाणि एवं विभक्तयः, उपसर्गाः एवं अव्ययानि, प्रत्ययप्रकरणम्, समासप्रकरणम्, वाच्यप्रकरणम्, संख्याज्ञानम्, शब्दज्ञानम् एवं अनुवादः, अपठितावबोधनम्, संस्कृतसाहित्यम् एवं काव्यशास्त्रम्, संस्कृतशिक्षणशास्त्रम्
  7. Language I/II — اردو / Urdu: رسم الخط، املا اور تلفظ, ذخیرۂ الفاظ, قواعد, محاورے اور ضرب الامثال, شعر و سخن, اردو ادب کی تاریخ, تفہیمِ عبارت, اردو کی تدریس
  8. Language I/II — বাংলা / Bengali: ভাষা, ধ্বনি ও বর্ণ, সন্ধি ও বানান, শব্দের উৎস ও গঠন, সমাস, পদ পরিচয়, কারক ও বিভক্তি, ক্রিয়া ও কাল, বাক্যতত্ত্ব, শব্দার্থ ও বাগর্থ, পাঠ অনুধাবন ও সাহিত্য, নির্মিতি ও পত্রলিখন, বাংলা শিক্ষণবিদ্যা
  9. Extra Practice (beyond syllabus) / अतिरिक्त अभ्यास (पाठ्यक्रम से बाहर): Computer Hardware and Peripherals / कंप्यूटर हार्डवेयर एवं परिधीय उपकरण, International Relations & Organisations / अंतरराष्ट्रीय संबंध एवं संगठन, Indian Economy: Data & Current Affairs / भारतीय अर्थव्यवस्था: आँकड़े एवं समसामयिकी
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

This educational video is a comprehensive lecture on the concept of 'Unit Digit' in number systems, presented by an instructor from Knowledge Gate Eduventures. The video begins with an introduction to the topic, emphasizing its importance for various competitive exams such as CAT, XAT, GMAT, and government tests, where it is a crucial part of the aptitude section. The core of the lecture focuses on a method to find the unit digit of large numbers raised to high powers. The instructor explains that this is achieved by identifying the cyclicity of the unit digit of the base number. The method involves observing the pattern of unit digits as the base is raised to successive powers. The video provides a classification of single-digit numbers (0-9) into three categories based on their cyclicity: numbers with a fixed unit digit (0, 1, 5, 6), numbers with a two-number cycle (4, 9), and numbers with a four-number cycle (2, 3, 7, 8). The instructor demonstrates this concept with several examples, including 185^563, 271^6987, and 156^25369, showing how to determine the unit digit by finding the remainder when the exponent is divided by the cycle length. The video concludes with a summary of the method and a list of practice problems for the viewer.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The video opens with a title slide for 'NUMBER SYSTEM' and a subtitle 'The mysterious world of numbers...'. The instructor, Yash Jain, introduces the topic, stating that it is a fundamental concept for various competitive exams. A slide titled 'Why Study This Topic?' lists numerous exams including CAT, XAT, CMAT, NMAT, SNAP, MAT, IIFT, GMAT, GATE, and others, emphasizing that number system is a crucial part of the aptitude section, with at least two questions appearing in every exam. The instructor is visible in a small window in the bottom right corner, speaking to the camera.

  2. 2:00 – 5:00 02:00-05:00

    The instructor continues to explain the importance of the topic, with a list of exams on the screen. He emphasizes that the number system is a key area for aptitude tests. The slide lists exams such as Placements, Government Exams, Civil Services Exams, Banking Exams, Railway Exams, College Entrance Exams, and others. The instructor's voiceover explains that this topic is essential for students preparing for these competitive exams. The visual focus remains on the list of exams, with the instructor's video feed in the corner.

  3. 5:00 – 10:00 05:00-10:00

    The video transitions to a new slide titled 'Concept of Unit Digit'. The instructor explains that to find the unit digit of a number raised to a power, one must understand the concept of cyclicity. He states that the unit digit of a number repeats in a pattern when the number is raised to successive powers. The slide shows an example: 'Unit Digit of 3547^153 x 251^72'. The instructor then moves to a new slide with a question: 'Q: Find the unit digit of the following:', followed by a list of 11 problems, including 185^563, 271^6987, and 154^258741369. The instructor begins to solve the first problem, 185^563, by focusing on the unit digit of the base, which is 5.

  4. 10:00 – 14:35 10:00-14:35

    The instructor explains the rule for numbers ending in 0, 1, 5, or 6: their unit digit remains the same regardless of the power. He demonstrates this with 185^563, stating the unit digit is 5. He then moves to 271^6987, noting the unit digit of the base is 1, so the answer is 1. For 156^25369, the unit digit is 6. The instructor then explains the cyclicity of 4 and 9, which have a cycle of 2. He demonstrates with 154^258741369, where the unit digit of the base is 4, and the exponent is odd, so the unit digit is 4. He then explains the cycle of 2, 3, 7, and 8, which have a cycle of 4. He demonstrates with 190^654789321, where the unit digit of the base is 0, so the answer is 0. The video ends with a 'Thank You for Watching' screen.

The video provides a structured and practical guide to solving unit digit problems, a common type of question in competitive exams. It begins by establishing the relevance of the topic, then systematically introduces the core concept of cyclicity. The instructor uses a clear, step-by-step approach, first explaining the rules for numbers with fixed unit digits (0, 1, 5, 6), then for those with a two-number cycle (4, 9), and finally for those with a four-number cycle (2, 3, 7, 8). The method is demonstrated through a series of worked examples, showing how to determine the cycle length and use the remainder of the exponent divided by the cycle length to find the correct unit digit. This logical progression from theory to application makes the concept accessible and provides a reliable method for students to solve similar problems under time pressure.

Loading lesson…